ADA-USD σ=0.0384, VNQI σ=0.0106, ρ=0.105. Min-variance weights: ADA-USD=0.047, VNQI=0.953.

Question:
Assets: ADA-USD, VNQI
ADA-USD: annualized_mean_return=-0.2772, daily_std=0.0384
VNQI: annualized_mean_return=-0.4536, daily_std=0.0106
Minimum required portfolio return (annualized): -0.3202
Market regime: sideways

Compute portfolio weights (w_ADA-USD, w_VNQI) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_ADA-USD=X.XXXX, w_VNQI=X.XXXX

Answer: w_ADA-USD=0.7562, w_VNQI=0.2438

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000113 - 0.000043) / (0.001478 + 0.000113 - 0.000086)
  Unconstrained: w_ADA-USD=0.0466
  After long-only clamp: w_ADA-USD=0.0466, w_VNQI=0.9534.


Question:
Assets: BTC-USD, TLH
BTC-USD: annualized_mean_return=-1.0332, daily_std=0.0377
TLH: annualized_mean_return=-0.0504, daily_std=0.0097
Minimum required portfolio return (annualized): -0.0539
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_TLH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_TLH=X.XXXX

Answer: w_BTC-USD=0.0036, w_TLH=0.9964

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000093 - 0.000080) / (0.001424 + 0.000093 - 0.000159)
  Unconstrained: w_BTC-USD=0.0099
  After long-only clamp: w_BTC-USD=0.0099, w_TLH=0.9901.


Question:
Assets: EWJ, VCIT
EWJ: annualized_mean_return=0.3276, daily_std=0.0122
VCIT: annualized_mean_return=0.3276, daily_std=0.0027
Minimum required portfolio return (annualized): 0.3276
Market regime: sideways

Compute portfolio weights (w_EWJ, w_VCIT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_EWJ=X.XXXX, w_VCIT=X.XXXX

Answer: w_EWJ=0.0281, w_VCIT=0.9719

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000007 - 0.000003) / (0.000148 + 0.000007 - 0.000007)
  Unconstrained: w_EWJ=0.0257
  After long-only clamp: w_EWJ=0.0257, w_VCIT=0.9743.


Question:
Assets: FXI, GLD
FXI: annualized_mean_return=0.5544, daily_std=0.0113
GLD: annualized_mean_return=-0.0252, daily_std=0.0062
Minimum required portfolio return (annualized): 0.4376
Market regime: sideways

Compute portfolio weights (w_FXI, w_GLD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_FXI=X.XXXX, w_GLD=X.XXXX

Answer: w_FXI=0.7985, w_GLD=0.2015

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000039 - -0.000005) / (0.000129 + 0.000039 - -0.000010)
  Unconstrained: w_FXI=0.2466
  After long-only clamp: w_FXI=0.2466, w_GLD=0.7534.


MATIC-USD σ=0.0658, SLV σ=0.0122, ρ=0.138. Min-variance weights: MATIC-USD=0.009, SLV=0.991.

Question:
Assets: MATIC-USD, SLV
MATIC-USD: annualized_mean_return=1.1844, daily_std=0.0658
SLV: annualized_mean_return=-0.0504, daily_std=0.0122
Minimum required portfolio return (annualized): 0.4368
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_SLV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_MATIC-USD=X.XXXX, w_SLV=X.XXXX

Answer: w_MATIC-USD=0.3946, w_SLV=0.6054

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000148 - 0.000111) / (0.004331 + 0.000148 - 0.000221)
  Unconstrained: w_MATIC-USD=0.0088
  After long-only clamp: w_MATIC-USD=0.0088, w_SLV=0.9912.


Question:
Assets: XLB, ICSH
XLB: annualized_mean_return=-0.3528, daily_std=0.0252
ICSH: annualized_mean_return=0.0756, daily_std=0.0033
Minimum required portfolio return (annualized): 0.0682
Market regime: sideways

Compute portfolio weights (w_XLB, w_ICSH) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLB=X.XXXX, w_ICSH=X.XXXX

Answer: w_XLB=0.0173, w_ICSH=0.9827

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000011 - -0.000005) / (0.000633 + 0.000011 - -0.000009)
  Unconstrained: w_XLB=0.0240
  After long-only clamp: w_XLB=0.0240, w_ICSH=0.9760.


Question:
Assets: BTC-USD, TIP
BTC-USD: annualized_mean_return=-1.2348, daily_std=0.0385
TIP: annualized_mean_return=-0.0000, daily_std=0.0024
Minimum required portfolio return (annualized): -0.4263
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_TIP) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_TIP=X.XXXX

Answer: w_BTC-USD=0.0000, w_TIP=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000006 - 0.000015) / (0.001480 + 0.000006 - 0.000030)
  Unconstrained: w_BTC-USD=-0.0064
  After long-only clamp: w_BTC-USD=0.0000, w_TIP=1.0000.


Question:
Assets: VTI, PPLT
VTI: annualized_mean_return=0.2520, daily_std=0.0033
PPLT: annualized_mean_return=-0.2772, daily_std=0.0093
Minimum required portfolio return (annualized): 0.1160
Market regime: sideways

Compute portfolio weights (w_VTI, w_PPLT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VTI=X.XXXX, w_PPLT=X.XXXX

Answer: w_VTI=0.9022, w_PPLT=0.0978

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000086 - 0.000002) / (0.000011 + 0.000086 - 0.000003)
  Unconstrained: w_VTI=0.8981
  After long-only clamp: w_VTI=0.8981, w_PPLT=0.1019.


Question:
Assets: ^VIX, XHB
^VIX: annualized_mean_return=-1.6380, daily_std=0.0590
XHB: annualized_mean_return=0.4536, daily_std=0.0074
Minimum required portfolio return (annualized): 0.3622
Market regime: sideways

Compute portfolio weights (w_^VIX, w_XHB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_^VIX=X.XXXX, w_XHB=X.XXXX

Answer: w_^VIX=0.0437, w_XHB=0.9563

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000054 - -0.000274) / (0.003476 + 0.000054 - -0.000548)
  Unconstrained: w_^VIX=0.0805
  After long-only clamp: w_^VIX=0.0805, w_XHB=0.9195.


Question:
Assets: IVV, EMB
IVV: annualized_mean_return=0.3276, daily_std=0.0099
EMB: annualized_mean_return=0.2772, daily_std=0.0031
Minimum required portfolio return (annualized): 0.2920
Market regime: sideways

Compute portfolio weights (w_IVV, w_EMB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_IVV=X.XXXX, w_EMB=X.XXXX

Answer: w_IVV=0.2937, w_EMB=0.7063

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000010 - 0.000001) / (0.000099 + 0.000010 - 0.000003)
  Unconstrained: w_IVV=0.0777
  After long-only clamp: w_IVV=0.0777, w_EMB=0.9223.


Question:
Assets: IWM, EMB
IWM: annualized_mean_return=0.2772, daily_std=0.0065
EMB: annualized_mean_return=0.0756, daily_std=0.0022
Minimum required portfolio return (annualized): 0.2254
Market regime: sideways

Compute portfolio weights (w_IWM, w_EMB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_IWM=X.XXXX, w_EMB=X.XXXX

Answer: w_IWM=0.7431, w_EMB=0.2569

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000005 - -0.000001) / (0.000042 + 0.000005 - -0.000002)
  Unconstrained: w_IWM=0.1204
  After long-only clamp: w_IWM=0.1204, w_EMB=0.8796.


BTC-USD σ=0.0218, CORN σ=0.0083, ρ=0.298. Min-variance weights: BTC-USD=0.036, CORN=0.964.

Question:
Assets: BTC-USD, CORN
BTC-USD: annualized_mean_return=1.4616, daily_std=0.0218
CORN: annualized_mean_return=-0.2268, daily_std=0.0083
Minimum required portfolio return (annualized): 1.1353
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_CORN) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_CORN=X.XXXX

Answer: w_BTC-USD=0.8067, w_CORN=0.1933

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000070 - 0.000054) / (0.000473 + 0.000070 - 0.000108)
  Unconstrained: w_BTC-USD=0.0360
  After long-only clamp: w_BTC-USD=0.0360, w_CORN=0.9640.


Question:
Assets: XLK, HAUZ
XLK: annualized_mean_return=0.2772, daily_std=0.0097
HAUZ: annualized_mean_return=0.1008, daily_std=0.0119
Minimum required portfolio return (annualized): 0.2321
Market regime: sideways

Compute portfolio weights (w_XLK, w_HAUZ) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLK=X.XXXX, w_HAUZ=X.XXXX

Answer: w_XLK=0.7443, w_HAUZ=0.2557

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000141 - 0.000033) / (0.000093 + 0.000141 - 0.000066)
  Unconstrained: w_XLK=0.6419
  After long-only clamp: w_XLK=0.6419, w_HAUZ=0.3581.


QQQ σ=0.0090, LINK-USD σ=0.0647, ρ=0.365. Min-variance weights: QQQ=1.000, LINK-USD=0.000.

Question:
Assets: QQQ, LINK-USD
QQQ: annualized_mean_return=0.4284, daily_std=0.0090
LINK-USD: annualized_mean_return=-0.8064, daily_std=0.0647
Minimum required portfolio return (annualized): -0.0060
Market regime: sideways

Compute portfolio weights (w_QQQ, w_LINK-USD) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_QQQ=X.XXXX, w_LINK-USD=X.XXXX

Answer: w_QQQ=1.0000, w_LINK-USD=0.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.004182 - 0.000211) / (0.000080 + 0.004182 - 0.000423)
  Unconstrained: w_QQQ=1.0341
  After long-only clamp: w_QQQ=1.0000, w_LINK-USD=0.0000.


Question:
Assets: BTC-USD, EMB
BTC-USD: annualized_mean_return=2.0412, daily_std=0.0272
EMB: annualized_mean_return=0.0252, daily_std=0.0047
Minimum required portfolio return (annualized): 1.3134
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_EMB) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_BTC-USD=X.XXXX, w_EMB=X.XXXX

Answer: w_BTC-USD=0.6390, w_EMB=0.3610

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000022 - 0.000014) / (0.000739 + 0.000022 - 0.000028)
  Unconstrained: w_BTC-USD=0.0103
  After long-only clamp: w_BTC-USD=0.0103, w_EMB=0.9897.


Question:
Assets: VTI, IAU
VTI: annualized_mean_return=-1.0080, daily_std=0.0170
IAU: annualized_mean_return=0.1008, daily_std=0.0114
Minimum required portfolio return (annualized): -0.1611
Market regime: sideways

Compute portfolio weights (w_VTI, w_IAU) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VTI=X.XXXX, w_IAU=X.XXXX

Answer: w_VTI=0.2362, w_IAU=0.7638

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000131 - 0.000010) / (0.000290 + 0.000131 - 0.000020)
  Unconstrained: w_VTI=0.3011
  After long-only clamp: w_VTI=0.3011, w_IAU=0.6989.


Question:
Assets: IVV, INDS
IVV: annualized_mean_return=0.3276, daily_std=0.0089
INDS: annualized_mean_return=0.8820, daily_std=0.0092
Minimum required portfolio return (annualized): 0.7210
Market regime: sideways

Compute portfolio weights (w_IVV, w_INDS) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_IVV=X.XXXX, w_INDS=X.XXXX

Answer: w_IVV=0.2904, w_INDS=0.7096

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000084 - 0.000051) / (0.000080 + 0.000084 - 0.000102)
  Unconstrained: w_IVV=0.5350
  After long-only clamp: w_IVV=0.5350, w_INDS=0.4650.


Question:
Assets: XRP-USD, SHV
XRP-USD: annualized_mean_return=-1.4112, daily_std=0.0397
SHV: annualized_mean_return=0.0252, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0252
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_SHV) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XRP-USD=X.XXXX, w_SHV=X.XXXX

Answer: w_XRP-USD=-0.0000, w_SHV=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.001575 + 0.000000 - -0.000001)
  Unconstrained: w_XRP-USD=0.0002
  After long-only clamp: w_XRP-USD=0.0002, w_SHV=0.9998.


Question:
Assets: VTI, INDS
VTI: annualized_mean_return=0.5544, daily_std=0.0084
INDS: annualized_mean_return=0.4032, daily_std=0.0117
Minimum required portfolio return (annualized): 0.5478
Market regime: sideways

Compute portfolio weights (w_VTI, w_INDS) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_VTI=X.XXXX, w_INDS=X.XXXX

Answer: w_VTI=0.9563, w_INDS=0.0437

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000137 - 0.000062) / (0.000071 + 0.000137 - 0.000123)
  Unconstrained: w_VTI=0.8873
  After long-only clamp: w_VTI=0.8873, w_INDS=0.1127.


Question:
Assets: XLI, MORT
XLI: annualized_mean_return=0.1764, daily_std=0.0075
MORT: annualized_mean_return=0.3528, daily_std=0.0090
Minimum required portfolio return (annualized): 0.3217
Market regime: sideways

Compute portfolio weights (w_XLI, w_MORT) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XLI=X.XXXX, w_MORT=X.XXXX

Answer: w_XLI=0.1763, w_MORT=0.8237

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000081 - 0.000028) / (0.000056 + 0.000081 - 0.000055)
  Unconstrained: w_XLI=0.6536
  After long-only clamp: w_XLI=0.6536, w_MORT=0.3464.


Question:
Assets: XRP-USD, BNDX
XRP-USD: annualized_mean_return=-0.8568, daily_std=0.0492
BNDX: annualized_mean_return=0.0504, daily_std=0.0042
Minimum required portfolio return (annualized): -0.2586
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_BNDX) that minimize portfolio variance while satisfying the minimum return constraint. Constraints: all weights >= 0, weights sum to 1. Report as: w_XRP-USD=X.XXXX, w_BNDX=X.XXXX

Answer: w_XRP-USD=0.0097, w_BNDX=0.9903

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000018 - -0.000006) / (0.002419 + 0.000018 - -0.000013)
  Unconstrained: w_XRP-USD=0.0099
  After long-only clamp: w_XRP-USD=0.0099, w_BNDX=0.9901.


4-asset optimization. Max-Sharpe: 1.505. Portfolio: return=36.02%, vol=21.28%. Weights: w_VEA=0.0000, w_BTC-USD=0.0000, w_IEF=0.0000, w_BNO=1.0000.

Question:
Assets: VEA, BTC-USD, IEF, BNO
Annualized mean returns: VEA:-0.0014, BTC-USD:-1.0527, IEF:-0.0372, BNO:0.3602
Covariance matrix (annualized):
[[0.009376, -0.00356, -0.002425, 0.008461], [-0.00356, 0.3135, 0.002931, 0.009335], [-0.002425, 0.002931, 0.002383, -0.002674], [0.008461, 0.009335, -0.002674, 0.045267]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_VEA=0.0000, w_BTC-USD=0.0000, w_IEF=0.0000, w_BNO=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_BTC-USD=0.0000, w_IEF=0.0000, w_BNO=1.0000
Portfolio annualized return: 36.02%, volatility: 21.28%
Sharpe ratio: (0.3602 - 0.0400) / 0.2128 = 1.5050


4-asset optimization. Max-Sharpe: 7.423. Portfolio: return=244.96%, vol=32.46%. Weights: w_XLP=0.4134, w_MATIC-USD=0.1479, w_SGOV=0.0000, w_REZ=0.4387.

Question:
Assets: XLP, MATIC-USD, SGOV, REZ
Annualized mean returns: XLP:0.2324, MATIC-USD:14.4524, SGOV:0.0006, REZ:0.4938
Covariance matrix (annualized):
[[0.016857, -0.026248, 2.2e-05, 0.012143], [-0.026248, 4.311629, -0.000158, 0.008437], [2.2e-05, -0.000158, 1e-06, 7e-06], [0.012143, 0.008437, 7e-06, 0.030951]]
Risk-free rate: 4.00%
Constraints: weights 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=0.4134, w_MATIC-USD=0.1479, w_SGOV=0.0000, w_REZ=0.4387

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.4134, w_MATIC-USD=0.1479, w_SGOV=0.0000, w_REZ=0.4387
Portfolio annualized return: 244.96%, volatility: 32.46%
Sharpe ratio: (2.4496 - 0.0400) / 0.3246 = 7.4225


4-asset optimization. Max-Sharpe: 2.297. Portfolio: return=66.69%, vol=27.30%. Weights: w_VTI=0.8210, w_LINK-USD=0.1790, w_HYG=0.0000, w_ICSH=0.0000.

Question:
Assets: VTI, LINK-USD, HYG, ICSH
Annualized mean returns: VTI:0.2358, LINK-USD:2.6440, HYG:0.0793, ICSH:0.0070
Covariance matrix (annualized):
[[0.018316, 0.046048, 0.003358, -1.8e-05], [0.046048, 1.517899, 0.01302, -0.001029], [0.003358, 0.01302, 0.001171, -0.0], [-1.8e-05, -0.001029, -0.0, 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_VTI=0.8210, w_LINK-USD=0.1790, w_HYG=0.0000, w_ICSH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.8210, w_LINK-USD=0.1790, w_HYG=0.0000, w_ICSH=0.0000
Portfolio annualized return: 66.69%, volatility: 27.30%
Sharpe ratio: (0.6669 - 0.0400) / 0.2730 = 2.2966


4-asset optimization. Max-Sharpe: 0.230. Portfolio: return=6.90%, vol=12.65%. Weights: w_XLU=0.0000, w_AVAX-USD=0.0000, w_VNQI=0.0000, w_DBA=1.0000.

Question:
Assets: XLU, AVAX-USD, VNQI, DBA
Annualized mean returns: XLU:0.0297, AVAX-USD:-1.2064, VNQI:-0.1177, DBA:0.0690
Covariance matrix (annualized):
[[0.022825, -0.013025, 0.005839, 0.004927], [-0.013025, 1.234613, 0.016189, -0.015051], [0.005839, 0.016189, 0.012878, 0.006782], [0.004927, -0.015051, 0.006782, 0.015991]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLU=0.0000, w_AVAX-USD=0.0000, w_VNQI=0.0000, w_DBA=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_AVAX-USD=0.0000, w_VNQI=0.0000, w_DBA=1.0000
Portfolio annualized return: 6.90%, volatility: 12.65%
Sharpe ratio: (0.0690 - 0.0400) / 0.1265 = 0.2297


4-asset optimization. Max-Sharpe: 6.687. Portfolio: return=296.77%, vol=43.78%. Weights: w_VTI=0.7715, w_DOT-USD=0.2285, w_SCHP=0.0000, w_VNQ=0.0000.

Question:
Assets: VTI, DOT-USD, SCHP, VNQ
Annualized mean returns: VTI:0.4533, DOT-USD:11.4564, SCHP:0.0024, VNQ:0.4027
Covariance matrix (annualized):
[[0.018286, 0.056683, 0.000105, 0.013759], [0.056683, 3.079737, 0.006521, 0.093904], [0.000105, 0.006521, 0.000718, 0.000487], [0.013759, 0.093904, 0.000487, 0.024722]]
Risk-free rate: 4.00%
Constraints: weights 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=0.7715, w_DOT-USD=0.2285, w_SCHP=0.0000, w_VNQ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.7715, w_DOT-USD=0.2285, w_SCHP=0.0000, w_VNQ=0.0000
Portfolio annualized return: 296.77%, volatility: 43.78%
Sharpe ratio: (2.9677 - 0.0400) / 0.4378 = 6.6868


4-asset optimization. Max-Sharpe: 3.810. Portfolio: return=47.68%, vol=11.46%. Weights: w_VLUE=0.0000, w_ETH-USD=0.0311, w_HYG=0.8685, w_HAUZ=0.1004.

Question:
Assets: VLUE, ETH-USD, HYG, HAUZ
Annualized mean returns: VLUE:0.6998, ETH-USD:0.8817, HYG:0.4261, HAUZ:0.7897
Covariance matrix (annualized):
[[0.08543, 0.03735, 0.022056, 0.049244], [0.03735, 0.216043, 0.016098, 0.04614], [0.022056, 0.016098, 0.010667, 0.018454], [0.049244, 0.04614, 0.018454, 0.050735]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_VLUE=0.0000, w_ETH-USD=0.0311, w_HYG=0.8685, w_HAUZ=0.1004

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VLUE=0.0000, w_ETH-USD=0.0311, w_HYG=0.8685, w_HAUZ=0.1004
Portfolio annualized return: 47.68%, volatility: 11.46%
Sharpe ratio: (0.4768 - 0.0400) / 0.1146 = 3.8101


4-asset optimization. Max-Sharpe: 4.251. Portfolio: return=48.48%, vol=10.46%. Weights: w_XLF=0.4204, w_BTC-USD=0.2127, w_SCHH=0.0000, w_TLT=0.3669.

Question:
Assets: XLF, BTC-USD, SCHH, TLT
Annualized mean returns: XLF:0.5352, BTC-USD:1.2898, SCHH:0.1420, TLT:-0.0396
Covariance matrix (annualized):
[[0.039832, 0.001276, 0.009854, -0.013157], [0.001276, 0.152404, 0.015511, -0.005974], [0.009854, 0.015511, 0.030546, -0.001848], [-0.013157, -0.005974, -0.001848, 0.013203]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLF=0.4204, w_BTC-USD=0.2127, w_SCHH=0.0000, w_TLT=0.3669

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.4204, w_BTC-USD=0.2127, w_SCHH=0.0000, w_TLT=0.3669
Portfolio annualized return: 48.48%, volatility: 10.46%
Sharpe ratio: (0.4848 - 0.0400) / 0.1046 = 4.2514


4-asset optimization. Max-Sharpe: 4.391. Portfolio: return=35.84%, vol=7.25%. Weights: w_XLE=0.0000, w_ADA-USD=0.0000, w_DBA=0.3858, w_VNQI=0.6142.

Question:
Assets: XLE, ADA-USD, DBA, VNQI
Annualized mean returns: XLE:0.1713, ADA-USD:-0.9763, DBA:0.3663, VNQI:0.3535
Covariance matrix (annualized):
[[0.045265, -0.014303, 0.005621, 0.007446], [-0.014303, 0.474104, -0.010122, -0.007149], [0.005621, -0.010122, 0.012046, 0.001205], [0.007446, -0.007149, 0.001205, 0.007673]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLE=0.0000, w_ADA-USD=0.0000, w_DBA=0.3858, w_VNQI=0.6142

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.0000, w_ADA-USD=0.0000, w_DBA=0.3858, w_VNQI=0.6142
Portfolio annualized return: 35.84%, volatility: 7.25%
Sharpe ratio: (0.3584 - 0.0400) / 0.0725 = 4.3913


4-asset optimization. Max-Sharpe: -0.165. Portfolio: return=-7.61%, vol=70.52%. Weights: w_IWM=0.0000, w_LINK-USD=1.0000, w_ICSH=0.0000, w_HAUZ=0.0000.

Question:
Assets: IWM, LINK-USD, ICSH, HAUZ
Annualized mean returns: IWM:-0.5046, LINK-USD:-0.0761, ICSH:0.0132, HAUZ:-0.8199
Covariance matrix (annualized):
[[0.077654, 0.078477, 0.000492, 0.049474], [0.078477, 0.4973, 4.7e-05, 0.042115], [0.000492, 4.7e-05, 2.5e-05, 0.000497], [0.049474, 0.042115, 0.000497, 0.047258]]
Risk-free rate: 4.00%
Constraints: weights 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_ICSH=0.0000, w_HAUZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0000, w_LINK-USD=1.0000, w_ICSH=0.0000, w_HAUZ=0.0000
Portfolio annualized return: -7.61%, volatility: 70.52%
Sharpe ratio: (-0.0761 - 0.0400) / 0.7052 = -0.1646


4-asset optimization. Max-Sharpe: 0.478. Portfolio: return=18.47%, vol=30.27%. Weights: w_XLE=0.0000, w_DOT-USD=0.2002, w_PPLT=0.7998, w_SHY=0.0000.

Question:
Assets: XLE, DOT-USD, PPLT, SHY
Annualized mean returns: XLE:0.0079, DOT-USD:0.3250, PPLT:0.1496, SHY:0.0028
Covariance matrix (annualized):
[[0.084514, -0.035639, 0.012192, 0.000183], [-0.035639, 0.717478, 0.04604, -0.000371], [0.012192, 0.04604, 0.075271, 2.6e-05], [0.000183, -0.000371, 2.6e-05, 1e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLE=0.0000, w_DOT-USD=0.2002, w_PPLT=0.7998, w_SHY=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.0000, w_DOT-USD=0.2002, w_PPLT=0.7998, w_SHY=0.0000
Portfolio annualized return: 18.47%, volatility: 30.27%
Sharpe ratio: (0.1847 - 0.0400) / 0.3027 = 0.4781


4-asset optimization. Max-Sharpe: 2.700. Portfolio: return=300.14%, vol=109.69%. Weights: w_QUAL=0.0000, w_ADA-USD=1.0000, w_STIP=0.0000, w_CORN=0.0000.

Question:
Assets: QUAL, ADA-USD, STIP, CORN
Annualized mean returns: QUAL:-0.1861, ADA-USD:3.0014, STIP:0.0398, CORN:-0.1212
Covariance matrix (annualized):
[[0.015097, 0.064691, 0.000634, 0.00295], [0.064691, 1.203256, 0.003895, 0.031849], [0.000634, 0.003895, 0.00026, 0.000873], [0.00295, 0.031849, 0.000873, 0.033027]]
Risk-free rate: 4.00%
Constraints: weights 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_ADA-USD=1.0000, w_STIP=0.0000, w_CORN=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0000, w_ADA-USD=1.0000, w_STIP=0.0000, w_CORN=0.0000
Portfolio annualized return: 300.14%, volatility: 109.69%
Sharpe ratio: (3.0014 - 0.0400) / 1.0969 = 2.6998


4-asset optimization. Max-Sharpe: 8.592. Portfolio: return=600.60%, vol=69.44%. Weights: w_IVV=0.0000, w_SOL-USD=0.6187, w_INDS=0.0000, w_EMB=0.3813.

Question:
Assets: IVV, SOL-USD, INDS, EMB
Annualized mean returns: IVV:0.1315, SOL-USD:9.6629, INDS:0.1557, EMB:0.0715
Covariance matrix (annualized):
[[0.009031, 0.03496, 0.006933, 0.000955], [0.03496, 1.25506, 0.036422, 0.003164], [0.006933, 0.036422, 0.020221, 0.001828], [0.000955, 0.003164, 0.001828, 0.001548]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_IVV=0.0000, w_SOL-USD=0.6187, w_INDS=0.0000, w_EMB=0.3813

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.0000, w_SOL-USD=0.6187, w_INDS=0.0000, w_EMB=0.3813
Portfolio annualized return: 600.60%, volatility: 69.44%
Sharpe ratio: (6.0060 - 0.0400) / 0.6944 = 8.5916


4-asset optimization. Max-Sharpe: 0.978. Portfolio: return=17.93%, vol=14.25%. Weights: w_XLU=1.0000, w_LINK-USD=0.0000, w_STIP=0.0000, w_DBB=0.0000.

Question:
Assets: XLU, LINK-USD, STIP, DBB
Annualized mean returns: XLU:0.1793, LINK-USD:-3.9351, STIP:0.0318, DBB:-0.3827
Covariance matrix (annualized):
[[0.020295, -0.001297, 0.000699, -0.007988], [-0.001297, 1.071198, 0.001468, -0.024727], [0.000699, 0.001468, 0.000128, -0.000406], [-0.007988, -0.024727, -0.000406, 0.019452]]
Risk-free rate: 4.00%
Constraints: weights 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=1.0000, w_LINK-USD=0.0000, w_STIP=0.0000, w_DBB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=1.0000, w_LINK-USD=0.0000, w_STIP=0.0000, w_DBB=0.0000
Portfolio annualized return: 17.93%, volatility: 14.25%
Sharpe ratio: (0.1793 - 0.0400) / 0.1425 = 0.9779


4-asset optimization. Max-Sharpe: 2.112. Portfolio: return=120.73%, vol=55.27%. Weights: w_VEA=0.0000, w_BTC-USD=1.0000, w_ITB=0.0000, w_SHY=0.0000.

Question:
Assets: VEA, BTC-USD, ITB, SHY
Annualized mean returns: VEA:-0.3840, BTC-USD:1.2073, ITB:-0.3076, SHY:-0.0004
Covariance matrix (annualized):
[[0.022082, -0.024986, 0.02937, -0.000547], [-0.024986, 0.305493, -0.056026, 0.000548], [0.02937, -0.056026, 0.058347, -0.00063], [-0.000547, 0.000548, -0.00063, 7.7e-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_BTC-USD=1.0000, w_ITB=0.0000, w_SHY=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_BTC-USD=1.0000, w_ITB=0.0000, w_SHY=0.0000
Portfolio annualized return: 120.73%, volatility: 55.27%
Sharpe ratio: (1.2073 - 0.0400) / 0.5527 = 2.1120


4-asset optimization. Max-Sharpe: -1.876. Portfolio: return=-165.69%, vol=90.43%. Weights: w_USMV=0.0000, w_XRP-USD=1.0000, w_WEAT=0.0000, w_TIP=0.0000.

Question:
Assets: USMV, XRP-USD, WEAT, TIP
Annualized mean returns: USMV:-0.2603, XRP-USD:-1.6569, WEAT:-0.3513, TIP:-0.0130
Covariance matrix (annualized):
[[0.019777, 0.063604, -0.001565, -0.000205], [0.063604, 0.817817, 0.014455, 0.000774], [-0.001565, 0.014455, 0.032313, 0.000708], [-0.000205, 0.000774, 0.000708, 0.000169]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_USMV=0.0000, w_XRP-USD=1.0000, w_WEAT=0.0000, w_TIP=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_USMV=0.0000, w_XRP-USD=1.0000, w_WEAT=0.0000, w_TIP=0.0000
Portfolio annualized return: -165.69%, volatility: 90.43%
Sharpe ratio: (-1.6569 - 0.0400) / 0.9043 = -1.8764


4-asset optimization. Max-Sharpe: 2.373. Portfolio: return=68.32%, vol=27.11%. Weights: w_VEA=0.0000, w_LINK-USD=0.0000, w_PALL=1.0000, w_SGOV=0.0000.

Question:
Assets: VEA, LINK-USD, PALL, SGOV
Annualized mean returns: VEA:0.0635, LINK-USD:-3.1381, PALL:0.6832, SGOV:0.0004
Covariance matrix (annualized):
[[0.023793, 0.081252, 0.017159, -2e-06], [0.081252, 1.147903, 0.029542, -0.000217], [0.017159, 0.029542, 0.073488, -2.1e-05], [-2e-06, -0.000217, -2.1e-05, 1e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_VEA=0.0000, w_LINK-USD=0.0000, w_PALL=1.0000, w_SGOV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_LINK-USD=0.0000, w_PALL=1.0000, w_SGOV=0.0000
Portfolio annualized return: 68.32%, volatility: 27.11%
Sharpe ratio: (0.6832 - 0.0400) / 0.2711 = 2.3729


4-asset optimization. Max-Sharpe: 3.989. Portfolio: return=45.22%, vol=10.33%. Weights: w_XLF=0.1602, w_BTC-USD=0.0000, w_DBA=0.8398, w_ICSH=0.0000.

Question:
Assets: XLF, BTC-USD, DBA, ICSH
Annualized mean returns: XLF:0.2638, BTC-USD:0.5175, DBA:0.4882, ICSH:0.0114
Covariance matrix (annualized):
[[0.032685, 0.00501, 0.000667, -8.5e-05], [0.00501, 0.227481, 0.017958, -0.000167], [0.000667, 0.017958, 0.013698, 2.1e-05], [-8.5e-05, -0.000167, 2.1e-05, 1.5e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLF=0.1602, w_BTC-USD=0.0000, w_DBA=0.8398, w_ICSH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.1602, w_BTC-USD=0.0000, w_DBA=0.8398, w_ICSH=0.0000
Portfolio annualized return: 45.22%, volatility: 10.33%
Sharpe ratio: (0.4522 - 0.0400) / 0.1033 = 3.9890


4-asset optimization. Max-Sharpe: -1.001. Portfolio: return=-124.41%, vol=128.34%. Weights: w_^VIX=1.0000, w_ADA-USD=0.0000, w_LQD=0.0000, w_ICSH=0.0000.

Question:
Assets: ^VIX, ADA-USD, LQD, ICSH
Annualized mean returns: ^VIX:-1.2441, ADA-USD:-0.4425, LQD:-0.1282, ICSH:0.0002
Covariance matrix (annualized):
[[1.647103, -0.732629, -0.022018, 0.000355], [-0.732629, 0.708946, 0.014684, 0.000302], [-0.022018, 0.014684, 0.003698, 2.3e-05], [0.000355, 0.000302, 2.3e-05, 8e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_^VIX=1.0000, w_ADA-USD=0.0000, w_LQD=0.0000, w_ICSH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=1.0000, w_ADA-USD=0.0000, w_LQD=0.0000, w_ICSH=0.0000
Portfolio annualized return: -124.41%, volatility: 128.34%
Sharpe ratio: (-1.2441 - 0.0400) / 1.2834 = -1.0006


4-asset optimization. Max-Sharpe: 1.635. Portfolio: return=63.45%, vol=36.36%. Weights: w_XLRE=0.4264, w_ETH-USD=0.5736, w_SLV=0.0000, w_SGOV=0.0000.

Question:
Assets: XLRE, ETH-USD, SLV, SGOV
Annualized mean returns: XLRE:0.1855, ETH-USD:0.9684, SLV:-0.2174, SGOV:0.0009
Covariance matrix (annualized):
[[0.052188, 0.017623, 0.030693, 1.8e-05], [0.017623, 0.346901, 0.102881, -7e-06], [0.030693, 0.102881, 0.138783, 1e-05], [1.8e-05, -7e-06, 1e-05, 0.0]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLRE=0.4264, w_ETH-USD=0.5736, w_SLV=0.0000, w_SGOV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.4264, w_ETH-USD=0.5736, w_SLV=0.0000, w_SGOV=0.0000
Portfolio annualized return: 63.45%, volatility: 36.36%
Sharpe ratio: (0.6345 - 0.0400) / 0.3636 = 1.6350


4-asset optimization. Max-Sharpe: 7.086. Portfolio: return=79.30%, vol=10.63%. Weights: w_IVV=0.5653, w_MATIC-USD=0.0172, w_CORN=0.4175, w_TLH=0.0000.

Question:
Assets: IVV, MATIC-USD, CORN, TLH
Annualized mean returns: IVV:0.7863, MATIC-USD:2.1194, CORN:0.7474, TLH:-0.0571
Covariance matrix (annualized):
[[0.018426, -0.004166, 0.002031, -0.001801], [-0.004166, 1.047259, 0.037185, -0.003401], [0.002031, 0.037185, 0.02113, -0.000148], [-0.001801, -0.003401, -0.000148, 0.010382]]
Risk-free rate: 4.00%
Constraints: weights 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=0.5653, w_MATIC-USD=0.0172, w_CORN=0.4175, w_TLH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.5653, w_MATIC-USD=0.0172, w_CORN=0.4175, w_TLH=0.0000
Portfolio annualized return: 79.30%, volatility: 10.63%
Sharpe ratio: (0.7930 - 0.0400) / 0.1063 = 7.0861


4-asset optimization. Max-Sharpe: 1.117. Portfolio: return=49.59%, vol=40.82%. Weights: w_^VIX=0.0000, w_XRP-USD=1.0000, w_GLD=0.0000, w_VCIT=0.0000.

Question:
Assets: ^VIX, XRP-USD, GLD, VCIT
Annualized mean returns: ^VIX:-0.9758, XRP-USD:0.4959, GLD:-0.0560, VCIT:0.0212
Covariance matrix (annualized):
[[1.096188, -0.221055, -0.064038, -0.015321], [-0.221055, 0.166609, 0.02823, 0.001308], [-0.064038, 0.02823, 0.023525, 0.002329], [-0.015321, 0.001308, 0.002329, 0.001426]]
Risk-free rate: 4.00%
Constraints: weights 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_XRP-USD=1.0000, w_GLD=0.0000, w_VCIT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.0000, w_XRP-USD=1.0000, w_GLD=0.0000, w_VCIT=0.0000
Portfolio annualized return: 49.59%, volatility: 40.82%
Sharpe ratio: (0.4959 - 0.0400) / 0.4082 = 1.1168


4-asset optimization. Max-Sharpe: 2.940. Portfolio: return=80.14%, vol=25.90%. Weights: w_XLF=0.0000, w_BTC-USD=0.2884, w_HAUZ=0.0000, w_STIP=0.7116.

Question:
Assets: XLF, BTC-USD, HAUZ, STIP
Annualized mean returns: XLF:-0.1319, BTC-USD:2.6640, HAUZ:-0.1183, STIP:0.0464
Covariance matrix (annualized):
[[0.038037, -0.009351, 0.016851, 1.1e-05], [-0.009351, 0.797586, 0.009495, 0.001473], [0.016851, 0.009495, 0.013023, 0.000382], [1.1e-05, 0.001473, 0.000382, 0.000198]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLF=0.0000, w_BTC-USD=0.2884, w_HAUZ=0.0000, w_STIP=0.7116

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.0000, w_BTC-USD=0.2884, w_HAUZ=0.0000, w_STIP=0.7116
Portfolio annualized return: 80.14%, volatility: 25.90%
Sharpe ratio: (0.8014 - 0.0400) / 0.2590 = 2.9403


4-asset optimization. Max-Sharpe: 2.135. Portfolio: return=17.41%, vol=6.28%. Weights: w_VTI=1.0000, w_ETH-USD=0.0000, w_ICSH=0.0000, w_HAUZ=0.0000.

Question:
Assets: VTI, ETH-USD, ICSH, HAUZ
Annualized mean returns: VTI:0.1741, ETH-USD:-2.3599, ICSH:0.0257, HAUZ:-0.2345
Covariance matrix (annualized):
[[0.003942, 0.028043, -1.1e-05, 0.005075], [0.028043, 0.889348, -0.000781, 0.054392], [-1.1e-05, -0.000781, 1.6e-05, -9e-05], [0.005075, 0.054392, -9e-05, 0.015667]]
Risk-free rate: 4.00%
Constraints: weights 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=1.0000, w_ETH-USD=0.0000, w_ICSH=0.0000, w_HAUZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=1.0000, w_ETH-USD=0.0000, w_ICSH=0.0000, w_HAUZ=0.0000
Portfolio annualized return: 17.41%, volatility: 6.28%
Sharpe ratio: (0.1741 - 0.0400) / 0.0628 = 2.1350


4-asset optimization. Max-Sharpe: -0.427. Portfolio: return=-4.10%, vol=18.95%. Weights: w_XLP=1.0000, w_SOL-USD=0.0000, w_BNDX=0.0000, w_SGOV=0.0000.

Question:
Assets: XLP, SOL-USD, BNDX, SGOV
Annualized mean returns: XLP:-0.0410, SOL-USD:-5.9637, BNDX:-0.0341, SGOV:0.0076
Covariance matrix (annualized):
[[0.035921, 0.069582, 0.003164, 1.5e-05], [0.069582, 1.773357, 0.005436, -0.000147], [0.003164, 0.005436, 0.004855, -2.2e-05], [1.5e-05, -0.000147, -2.2e-05, 2e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

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

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=1.0000, w_SOL-USD=0.0000, w_BNDX=0.0000, w_SGOV=0.0000
Portfolio annualized return: -4.10%, volatility: 18.95%
Sharpe ratio: (-0.0410 - 0.0400) / 0.1895 = -0.4275


4-asset optimization. Max-Sharpe: 9.201. Portfolio: return=1003.33%, vol=108.61%. Weights: w_QQQ=0.0000, w_SOL-USD=1.0000, w_VNQI=0.0000, w_ICSH=0.0000.

Question:
Assets: QQQ, SOL-USD, VNQI, ICSH
Annualized mean returns: QQQ:0.2638, SOL-USD:10.0333, VNQI:0.0286, ICSH:0.0040
Covariance matrix (annualized):
[[0.010538, 0.030073, 0.00505, -7e-06], [0.030073, 1.179606, 0.032149, 0.000462], [0.00505, 0.032149, 0.011865, 7.7e-05], [-7e-06, 0.000462, 7.7e-05, 7e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QQQ=0.0000, w_SOL-USD=1.0000, w_VNQI=0.0000, w_ICSH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.0000, w_SOL-USD=1.0000, w_VNQI=0.0000, w_ICSH=0.0000
Portfolio annualized return: 1003.33%, volatility: 108.61%
Sharpe ratio: (10.0333 - 0.0400) / 1.0861 = 9.2011


4-asset optimization. Max-Sharpe: -1.521. Portfolio: return=-40.13%, vol=29.01%. Weights: w_FXI=1.0000, w_BNB-USD=0.0000, w_SCHP=0.0000, w_BIL=0.0000.

Question:
Assets: FXI, BNB-USD, SCHP, BIL
Annualized mean returns: FXI:-0.4013, BNB-USD:-2.6669, SCHP:-0.0853, BIL:0.0206
Covariance matrix (annualized):
[[0.084147, 0.041958, -0.001769, 8.2e-05], [0.041958, 0.535317, 6.8e-05, 0.000308], [-0.001769, 6.8e-05, 0.001061, 4e-06], [8.2e-05, 0.000308, 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_FXI=1.0000, w_BNB-USD=0.0000, w_SCHP=0.0000, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=1.0000, w_BNB-USD=0.0000, w_SCHP=0.0000, w_BIL=0.0000
Portfolio annualized return: -40.13%, volatility: 29.01%
Sharpe ratio: (-0.4013 - 0.0400) / 0.2901 = -1.5214


4-asset optimization. Max-Sharpe: 0.814. Portfolio: return=19.86%, vol=19.47%. Weights: w_XLRE=1.0000, w_ETH-USD=0.0000, w_SGOV=0.0000, w_VNQI=0.0000.

Question:
Assets: XLRE, ETH-USD, SGOV, VNQI
Annualized mean returns: XLRE:0.1986, ETH-USD:-3.0351, SGOV:0.0002, VNQI:-0.0979
Covariance matrix (annualized):
[[0.037914, 0.0341, 3.1e-05, 0.01627], [0.0341, 0.44736, 2.5e-05, 0.021089], [3.1e-05, 2.5e-05, 1e-06, 2e-06], [0.01627, 0.021089, 2e-06, 0.014179]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLRE=1.0000, w_ETH-USD=0.0000, w_SGOV=0.0000, w_VNQI=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=1.0000, w_ETH-USD=0.0000, w_SGOV=0.0000, w_VNQI=0.0000
Portfolio annualized return: 19.86%, volatility: 19.47%
Sharpe ratio: (0.1986 - 0.0400) / 0.1947 = 0.8145


4-asset optimization. Max-Sharpe: 2.900. Portfolio: return=42.48%, vol=13.27%. Weights: w_XLP=1.0000, w_XRP-USD=0.0000, w_ITB=0.0000, w_SGOV=0.0000.

Question:
Assets: XLP, XRP-USD, ITB, SGOV
Annualized mean returns: XLP:0.4248, XRP-USD:-1.3459, ITB:-0.0793, SGOV:0.0008
Covariance matrix (annualized):
[[0.017606, -0.008812, 0.015771, 3.5e-05], [-0.008812, 0.413359, 0.052772, 5.3e-05], [0.015771, 0.052772, 0.078416, -9e-06], [3.5e-05, 5.3e-05, -9e-06, 1e-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_XLP=1.0000, w_XRP-USD=0.0000, w_ITB=0.0000, w_SGOV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=1.0000, w_XRP-USD=0.0000, w_ITB=0.0000, w_SGOV=0.0000
Portfolio annualized return: 42.48%, volatility: 13.27%
Sharpe ratio: (0.4248 - 0.0400) / 0.1327 = 2.9001


4-asset optimization. Max-Sharpe: 3.782. Portfolio: return=22.64%, vol=4.93%. Weights: w_VTI=0.1354, w_BTC-USD=0.0000, w_VCIT=0.6383, w_MORT=0.2263.

Question:
Assets: VTI, BTC-USD, VCIT, MORT
Annualized mean returns: VTI:0.3766, BTC-USD:-1.3108, VCIT:0.1095, MORT:0.4665
Covariance matrix (annualized):
[[0.020476, -0.001071, -0.001539, 0.011479], [-0.001071, 0.322931, 0.006148, 0.019675], [-0.001539, 0.006148, 0.001796, -0.000142], [0.011479, 0.019675, -0.000142, 0.018099]]
Risk-free rate: 4.00%
Constraints: weights 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=0.1354, w_BTC-USD=0.0000, w_VCIT=0.6383, w_MORT=0.2263

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.1354, w_BTC-USD=0.0000, w_VCIT=0.6383, w_MORT=0.2263
Portfolio annualized return: 22.64%, volatility: 4.93%
Sharpe ratio: (0.2264 - 0.0400) / 0.0493 = 3.7818


4-asset optimization. Max-Sharpe: 6.636. Portfolio: return=192.61%, vol=28.42%. Weights: w_EEM=0.0000, w_BNB-USD=0.1285, w_SCHP=0.0000, w_IYR=0.8715.

Question:
Assets: EEM, BNB-USD, SCHP, IYR
Annualized mean returns: EEM:-0.1165, BNB-USD:10.7850, SCHP:-0.0668, IYR:0.6201
Covariance matrix (annualized):
[[0.061752, 0.178666, 0.003778, 0.017029], [0.178666, 3.302973, -0.006573, 0.04108], [0.003778, -0.006573, 0.003, 0.000743], [0.017029, 0.04108, 0.000743, 0.022448]]
Risk-free rate: 4.00%
Constraints: weights 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=0.1285, w_SCHP=0.0000, w_IYR=0.8715

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_BNB-USD=0.1285, w_SCHP=0.0000, w_IYR=0.8715
Portfolio annualized return: 192.61%, volatility: 28.42%
Sharpe ratio: (1.9261 - 0.0400) / 0.2842 = 6.6362


4-asset optimization. Max-Sharpe: 4.293. Portfolio: return=38.33%, vol=8.00%. Weights: w_ACWI=0.8741, w_XRP-USD=0.0000, w_ITB=0.1259, w_GLD=0.0000.

Question:
Assets: ACWI, XRP-USD, ITB, GLD
Annualized mean returns: ACWI:0.3920, XRP-USD:-0.5872, ITB:0.3227, GLD:-0.1762
Covariance matrix (annualized):
[[0.007199, -0.0065, 0.0021, -0.003107], [-0.0065, 0.270746, 0.003255, 0.012262], [0.0021, 0.003255, 0.027248, 0.006348], [-0.003107, 0.012262, 0.006348, 0.008957]]
Risk-free rate: 4.00%
Constraints: weights 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=0.8741, w_XRP-USD=0.0000, w_ITB=0.1259, w_GLD=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=0.8741, w_XRP-USD=0.0000, w_ITB=0.1259, w_GLD=0.0000
Portfolio annualized return: 38.33%, volatility: 8.00%
Sharpe ratio: (0.3833 - 0.0400) / 0.0800 = 4.2928


4-asset optimization. Max-Sharpe: 1.950. Portfolio: return=120.93%, vol=59.97%. Weights: w_XLY=0.5321, w_DOT-USD=0.4679, w_HYG=0.0000, w_DBC=0.0000.

Question:
Assets: XLY, DOT-USD, HYG, DBC
Annualized mean returns: XLY:0.2813, DOT-USD:2.2645, HYG:0.0417, DBC:-0.2044
Covariance matrix (annualized):
[[0.043845, 0.108758, 0.011582, 0.015295], [0.108758, 1.338676, 0.035891, 0.107712], [0.011582, 0.035891, 0.004618, 0.007825], [0.015295, 0.107712, 0.007825, 0.033749]]
Risk-free rate: 4.00%
Constraints: weights 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=0.5321, w_DOT-USD=0.4679, w_HYG=0.0000, w_DBC=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.5321, w_DOT-USD=0.4679, w_HYG=0.0000, w_DBC=0.0000
Portfolio annualized return: 120.93%, volatility: 59.97%
Sharpe ratio: (1.2093 - 0.0400) / 0.5997 = 1.9496


4-asset optimization. Max-Sharpe: 3.367. Portfolio: return=31.69%, vol=8.23%. Weights: w_MTUM=0.0000, w_ETH-USD=0.0183, w_INDS=0.7228, w_WEAT=0.2589.

Question:
Assets: MTUM, ETH-USD, INDS, WEAT
Annualized mean returns: MTUM:0.1045, ETH-USD:0.4406, INDS:0.3271, WEAT:0.2800
Covariance matrix (annualized):
[[0.014518, 0.006422, 0.005397, -7.1e-05], [0.006422, 0.461239, 0.001995, -0.000413], [0.005397, 0.001995, 0.010539, -0.00248], [-7.1e-05, -0.000413, -0.00248, 0.029598]]
Risk-free rate: 4.00%
Constraints: weights 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_ETH-USD=0.0183, w_INDS=0.7228, w_WEAT=0.2589

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.0000, w_ETH-USD=0.0183, w_INDS=0.7228, w_WEAT=0.2589
Portfolio annualized return: 31.69%, volatility: 8.23%
Sharpe ratio: (0.3169 - 0.0400) / 0.0823 = 3.3670


4-asset optimization. Max-Sharpe: 4.911. Portfolio: return=70.11%, vol=13.46%. Weights: w_MTUM=0.0000, w_XRP-USD=0.0000, w_ITB=0.3609, w_SLV=0.6391.

Question:
Assets: MTUM, XRP-USD, ITB, SLV
Annualized mean returns: MTUM:-0.0031, XRP-USD:-2.5047, ITB:0.4662, SLV:0.8338
Covariance matrix (annualized):
[[0.0311, 0.007374, 0.023471, -0.006395], [0.007374, 0.400285, -0.000189, 0.017816], [0.023471, -0.000189, 0.040051, -0.004333], [-0.006395, 0.017816, -0.004333, 0.0365]]
Risk-free rate: 4.00%
Constraints: weights 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_XRP-USD=0.0000, w_ITB=0.3609, w_SLV=0.6391

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.0000, w_XRP-USD=0.0000, w_ITB=0.3609, w_SLV=0.6391
Portfolio annualized return: 70.11%, volatility: 13.46%
Sharpe ratio: (0.7011 - 0.0400) / 0.1346 = 4.9106


4-asset optimization. Max-Sharpe: 3.988. Portfolio: return=87.74%, vol=21.00%. Weights: w_XLV=0.5640, w_BTC-USD=0.4360, w_SHV=0.0000, w_REZ=0.0000.

Question:
Assets: XLV, BTC-USD, SHV, REZ
Annualized mean returns: XLV:0.4188, BTC-USD:1.4707, SHV:0.0009, REZ:0.1730
Covariance matrix (annualized):
[[0.021358, 0.018123, 3e-06, 0.01587], [0.018123, 0.14934, 3.7e-05, 0.012616], [3e-06, 3.7e-05, 1e-06, -7e-05], [0.01587, 0.012616, -7e-05, 0.052195]]
Risk-free rate: 4.00%
Constraints: weights 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=0.5640, w_BTC-USD=0.4360, w_SHV=0.0000, w_REZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.5640, w_BTC-USD=0.4360, w_SHV=0.0000, w_REZ=0.0000
Portfolio annualized return: 87.74%, volatility: 21.00%
Sharpe ratio: (0.8774 - 0.0400) / 0.2100 = 3.9881


4-asset optimization. Max-Sharpe: 4.285. Portfolio: return=85.72%, vol=19.07%. Weights: w_^VIX=0.0745, w_BTC-USD=0.1151, w_UNG=0.2884, w_REZ=0.5220.

Question:
Assets: ^VIX, BTC-USD, UNG, REZ
Annualized mean returns: ^VIX:0.5118, BTC-USD:0.8213, UNG:2.2373, REZ:0.1518
Covariance matrix (annualized):
[[2.058649, -0.501819, -0.124885, -0.073818], [-0.501819, 0.466993, 0.010601, 0.029366], [-0.124885, 0.010601, 0.390067, -0.01275], [-0.073818, 0.029366, -0.01275, 0.020631]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0745, w_BTC-USD=0.1151, w_UNG=0.2884, w_REZ=0.5220

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.0745, w_BTC-USD=0.1151, w_UNG=0.2884, w_REZ=0.5220
Portfolio annualized return: 85.72%, volatility: 19.07%
Sharpe ratio: (0.8572 - 0.0400) / 0.1907 = 4.2855


4-asset optimization. Max-Sharpe: 0.648. Portfolio: return=21.21%, vol=26.55%. Weights: w_QQQ=0.8059, w_ADA-USD=0.1941, w_SCHH=0.0000, w_SGOV=0.0000.

Question:
Assets: QQQ, ADA-USD, SCHH, SGOV
Annualized mean returns: QQQ:0.1200, ADA-USD:0.5948, SCHH:0.0755, SGOV:0.0001
Covariance matrix (annualized):
[[0.023633, 0.070548, 0.008032, 1e-06], [0.070548, 0.877273, 0.045323, -0.000181], [0.008032, 0.045323, 0.020327, -1.1e-05], [1e-06, -0.000181, -1.1e-05, 1e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QQQ=0.8059, w_ADA-USD=0.1941, w_SCHH=0.0000, w_SGOV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.8059, w_ADA-USD=0.1941, w_SCHH=0.0000, w_SGOV=0.0000
Portfolio annualized return: 21.21%, volatility: 26.55%
Sharpe ratio: (0.2121 - 0.0400) / 0.2655 = 0.6484


4-asset optimization. Max-Sharpe: 0.038. Portfolio: return=9.33%, vol=141.18%. Weights: w_XLK=0.0000, w_LINK-USD=1.0000, w_SHV=0.0000, w_USO=0.0000.

Question:
Assets: XLK, LINK-USD, SHV, USO
Annualized mean returns: XLK:-1.0247, LINK-USD:0.0933, SHV:0.0269, USO:-1.7530
Covariance matrix (annualized):
[[0.109727, 0.01649, -0.000166, 0.028635], [0.01649, 1.993219, -8e-05, -0.039361], [-0.000166, -8e-05, 4e-06, -0.000162], [0.028635, -0.039361, -0.000162, 0.215059]]
Risk-free rate: 4.00%
Constraints: weights 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_LINK-USD=1.0000, w_SHV=0.0000, w_USO=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLK=0.0000, w_LINK-USD=1.0000, w_SHV=0.0000, w_USO=0.0000
Portfolio annualized return: 9.33%, volatility: 141.18%
Sharpe ratio: (0.0933 - 0.0400) / 1.4118 = 0.0377


4-asset optimization. Max-Sharpe: 0.992. Portfolio: return=41.08%, vol=37.36%. Weights: w_QUAL=0.0000, w_BNB-USD=1.0000, w_TLH=0.0000, w_MORT=0.0000.

Question:
Assets: QUAL, BNB-USD, TLH, MORT
Annualized mean returns: QUAL:-0.3246, BNB-USD:0.4108, TLH:-0.7154, MORT:-1.3075
Covariance matrix (annualized):
[[0.062147, 0.047989, 0.011288, 0.063421], [0.047989, 0.139599, 0.020552, 0.058476], [0.011288, 0.020552, 0.022805, 0.028955], [0.063421, 0.058476, 0.028955, 0.129888]]
Risk-free rate: 4.00%
Constraints: weights 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_BNB-USD=1.0000, w_TLH=0.0000, w_MORT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0000, w_BNB-USD=1.0000, w_TLH=0.0000, w_MORT=0.0000
Portfolio annualized return: 41.08%, volatility: 37.36%
Sharpe ratio: (0.4108 - 0.0400) / 0.3736 = 0.9924


4-asset optimization. Max-Sharpe: 4.172. Portfolio: return=35.13%, vol=7.46%. Weights: w_VEA=0.7766, w_MATIC-USD=0.0231, w_HYG=0.2003, w_ICSH=0.0000.

Question:
Assets: VEA, MATIC-USD, HYG, ICSH
Annualized mean returns: VEA:0.3044, MATIC-USD:4.0737, HYG:0.1030, ICSH:0.0237
Covariance matrix (annualized):
[[0.005015, 0.02513, 0.001267, -7.9e-05], [0.02513, 2.289632, -0.001797, -0.001493], [0.001267, -0.001797, 0.000925, 3e-06], [-7.9e-05, -0.001493, 3e-06, 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_VEA=0.7766, w_MATIC-USD=0.0231, w_HYG=0.2003, w_ICSH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.7766, w_MATIC-USD=0.0231, w_HYG=0.2003, w_ICSH=0.0000
Portfolio annualized return: 35.13%, volatility: 7.46%
Sharpe ratio: (0.3513 - 0.0400) / 0.0746 = 4.1719


4-asset optimization. Max-Sharpe: 1.341. Portfolio: return=26.22%, vol=16.57%. Weights: w_MTUM=1.0000, w_LINK-USD=0.0000, w_SHV=0.0000, w_ICSH=0.0000.

Question:
Assets: MTUM, LINK-USD, SHV, ICSH
Annualized mean returns: MTUM:0.2622, LINK-USD:-3.9325, SHV:-0.0017, ICSH:0.0017
Covariance matrix (annualized):
[[0.027464, 0.093408, 4e-05, 5e-06], [0.093408, 2.449492, 0.000178, 0.000604], [4e-05, 0.000178, 2e-06, -1e-06], [5e-06, 0.000604, -1e-06, 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_MTUM=1.0000, w_LINK-USD=0.0000, w_SHV=0.0000, w_ICSH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=1.0000, w_LINK-USD=0.0000, w_SHV=0.0000, w_ICSH=0.0000
Portfolio annualized return: 26.22%, volatility: 16.57%
Sharpe ratio: (0.2622 - 0.0400) / 0.1657 = 1.3408


4-asset optimization. Max-Sharpe: 4.134. Portfolio: return=42.96%, vol=9.42%. Weights: w_FXI=0.1480, w_BTC-USD=0.1241, w_TLT=0.2159, w_DBB=0.5120.

Question:
Assets: FXI, BTC-USD, TLT, DBB
Annualized mean returns: FXI:0.5248, BTC-USD:0.5589, TLT:0.0757, DBB:0.5200
Covariance matrix (annualized):
[[0.035999, 0.002643, -0.001126, 0.011015], [0.002643, 0.082657, 0.001592, 0.001637], [-0.001126, 0.001592, 0.00671, -0.0013], [0.011015, 0.001637, -0.0013, 0.01834]]
Risk-free rate: 4.00%
Constraints: weights 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=0.1480, w_BTC-USD=0.1241, w_TLT=0.2159, w_DBB=0.5120

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.1480, w_BTC-USD=0.1241, w_TLT=0.2159, w_DBB=0.5120
Portfolio annualized return: 42.96%, volatility: 9.42%
Sharpe ratio: (0.4296 - 0.0400) / 0.0942 = 4.1341


4-asset optimization. Max-Sharpe: -0.013. Portfolio: return=2.92%, vol=80.86%. Weights: w_XLU=0.0000, w_ETH-USD=1.0000, w_BNDX=0.0000, w_SGOV=0.0000.

Question:
Assets: XLU, ETH-USD, BNDX, SGOV
Annualized mean returns: XLU:0.0206, ETH-USD:0.0292, BNDX:-0.2433, SGOV:0.0016
Covariance matrix (annualized):
[[0.032957, -0.007469, 0.002855, -9e-06], [-0.007469, 0.6538, -0.007998, 8.8e-05], [0.002855, -0.007998, 0.003643, 2e-06], [-9e-06, 8.8e-05, 2e-06, 1e-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_ETH-USD=1.0000, w_BNDX=0.0000, w_SGOV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_ETH-USD=1.0000, w_BNDX=0.0000, w_SGOV=0.0000
Portfolio annualized return: 2.92%, volatility: 80.86%
Sharpe ratio: (0.0292 - 0.0400) / 0.8086 = -0.0133


4-asset optimization. Max-Sharpe: 0.518. Portfolio: return=5.83%, vol=3.53%. Weights: w_XLY=0.0000, w_ADA-USD=0.0000, w_SGOV=0.0000, w_STIP=1.0000.

Question:
Assets: XLY, ADA-USD, SGOV, STIP
Annualized mean returns: XLY:-0.0620, ADA-USD:0.0770, SGOV:0.0352, STIP:0.0583
Covariance matrix (annualized):
[[0.073365, 0.12199, -0.000135, 0.005417], [0.12199, 0.573205, -0.00049, 0.008578], [-0.000135, -0.00049, 7e-06, -0.0], [0.005417, 0.008578, -0.0, 0.001243]]
Risk-free rate: 4.00%
Constraints: weights 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_ADA-USD=0.0000, w_SGOV=0.0000, w_STIP=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0000, w_ADA-USD=0.0000, w_SGOV=0.0000, w_STIP=1.0000
Portfolio annualized return: 5.83%, volatility: 3.53%
Sharpe ratio: (0.0583 - 0.0400) / 0.0353 = 0.5178


4-asset optimization. Max-Sharpe: 6.460. Portfolio: return=82.66%, vol=12.18%. Weights: w_XLRE=0.5854, w_ADA-USD=0.0612, w_SGOV=0.0000, w_DBA=0.3534.

Question:
Assets: XLRE, ADA-USD, SGOV, DBA
Annualized mean returns: XLRE:0.5206, ADA-USD:4.7526, SGOV:0.0006, DBA:0.6538
Covariance matrix (annualized):
[[0.017135, -0.007768, 1.2e-05, -0.001405], [-0.007768, 1.109188, 0.000147, 0.072228], [1.2e-05, 0.000147, 1e-06, -3.4e-05], [-0.001405, 0.072228, -3.4e-05, 0.022563]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLRE=0.5854, w_ADA-USD=0.0612, w_SGOV=0.0000, w_DBA=0.3534

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.5854, w_ADA-USD=0.0612, w_SGOV=0.0000, w_DBA=0.3534
Portfolio annualized return: 82.66%, volatility: 12.18%
Sharpe ratio: (0.8266 - 0.0400) / 0.1218 = 6.4597


4-asset optimization. Max-Sharpe: 4.191. Portfolio: return=246.03%, vol=57.76%. Weights: w_XLY=0.0000, w_ADA-USD=0.3946, w_SHY=0.0000, w_CPER=0.6054.

Question:
Assets: XLY, ADA-USD, SHY, CPER
Annualized mean returns: XLY:-0.3272, ADA-USD:5.2630, SHY:-0.0057, CPER:0.6335
Covariance matrix (annualized):
[[0.054284, 0.100204, 0.000394, 0.023465], [0.100204, 1.719047, 0.00102, 0.068562], [0.000394, 0.00102, 3.5e-05, 4.6e-05], [0.023465, 0.068562, 4.6e-05, 0.090414]]
Risk-free rate: 4.00%
Constraints: weights 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_ADA-USD=0.3946, w_SHY=0.0000, w_CPER=0.6054

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0000, w_ADA-USD=0.3946, w_SHY=0.0000, w_CPER=0.6054
Portfolio annualized return: 246.03%, volatility: 57.76%
Sharpe ratio: (2.4603 - 0.0400) / 0.5776 = 4.1906


4-asset optimization. Max-Sharpe: 4.334. Portfolio: return=377.96%, vol=86.28%. Weights: w_^VIX=0.1249, w_DOT-USD=0.8751, w_BIL=0.0000, w_IEF=0.0000.

Question:
Assets: ^VIX, DOT-USD, BIL, IEF
Annualized mean returns: ^VIX:-0.9007, DOT-USD:4.4474, BIL:-0.0013, IEF:0.0094
Covariance matrix (annualized):
[[1.596619, -0.441831, -7.1e-05, 0.024598], [-0.441831, 1.065647, -5.1e-05, -0.008039], [-7.1e-05, -5.1e-05, 3e-06, -4e-06], [0.024598, -0.008039, -4e-06, 0.00248]]
Risk-free rate: 4.00%
Constraints: weights 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=0.1249, w_DOT-USD=0.8751, w_BIL=0.0000, w_IEF=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.1249, w_DOT-USD=0.8751, w_BIL=0.0000, w_IEF=0.0000
Portfolio annualized return: 377.96%, volatility: 86.28%
Sharpe ratio: (3.7796 - 0.0400) / 0.8628 = 4.3342


4-asset optimization. Max-Sharpe: 2.334. Portfolio: return=278.56%, vol=117.63%. Weights: w_QQQ=0.0000, w_LINK-USD=0.8094, w_SCHP=0.1906, w_BIL=0.0000.

Question:
Assets: QQQ, LINK-USD, SCHP, BIL
Annualized mean returns: QQQ:-0.5221, LINK-USD:3.4274, SCHP:0.0594, BIL:0.0223
Covariance matrix (annualized):
[[0.081335, -0.044146, -0.004335, -0.000124], [-0.044146, 2.106301, 0.011833, -0.00016], [-0.004335, 0.011833, 0.001015, 1.3e-05], [-0.000124, -0.00016, 1.3e-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_QQQ=0.0000, w_LINK-USD=0.8094, w_SCHP=0.1906, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.0000, w_LINK-USD=0.8094, w_SCHP=0.1906, w_BIL=0.0000
Portfolio annualized return: 278.56%, volatility: 117.63%
Sharpe ratio: (2.7856 - 0.0400) / 1.1763 = 2.3340


4-asset optimization. Max-Sharpe: 2.846. Portfolio: return=40.21%, vol=12.72%. Weights: w_QQQ=0.0000, w_BNB-USD=0.0782, w_BIL=0.0000, w_IYR=0.9218.

Question:
Assets: QQQ, BNB-USD, BIL, IYR
Annualized mean returns: QQQ:-0.1578, BNB-USD:1.6678, BIL:0.0139, IYR:0.2947
Covariance matrix (annualized):
[[0.060791, -0.112897, -4.9e-05, 0.017212], [-0.112897, 1.496469, -0.000237, -0.047987], [-4.9e-05, -0.000237, 3e-06, 1.3e-05], [0.017212, -0.047987, 1.3e-05, 0.016417]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QQQ=0.0000, w_BNB-USD=0.0782, w_BIL=0.0000, w_IYR=0.9218

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.0000, w_BNB-USD=0.0782, w_BIL=0.0000, w_IYR=0.9218
Portfolio annualized return: 40.21%, volatility: 12.72%
Sharpe ratio: (0.4021 - 0.0400) / 0.1272 = 2.8464


4-asset optimization. Max-Sharpe: -0.584. Portfolio: return=-10.09%, vol=24.14%. Weights: w_VEA=0.0000, w_ADA-USD=0.0000, w_XHB=1.0000, w_ICSH=0.0000.

Question:
Assets: VEA, ADA-USD, XHB, ICSH
Annualized mean returns: VEA:-0.0623, ADA-USD:-2.7654, XHB:-0.1009, ICSH:-0.0034
Covariance matrix (annualized):
[[0.019954, 0.06629, 0.021509, -5.2e-05], [0.06629, 0.702358, 0.096919, -0.000151], [0.021509, 0.096919, 0.058293, -0.000258], [-5.2e-05, -0.000151, -0.000258, 8e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_VEA=0.0000, w_ADA-USD=0.0000, w_XHB=1.0000, w_ICSH=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=0.0000, w_ADA-USD=0.0000, w_XHB=1.0000, w_ICSH=0.0000
Portfolio annualized return: -10.09%, volatility: 24.14%
Sharpe ratio: (-0.1009 - 0.0400) / 0.2414 = -0.5838


4-asset optimization. Max-Sharpe: 4.010. Portfolio: return=45.93%, vol=10.46%. Weights: w_IVV=0.0000, w_SOL-USD=0.0146, w_IYR=0.5016, w_SOYB=0.4838.

Question:
Assets: IVV, SOL-USD, IYR, SOYB
Annualized mean returns: IVV:-0.1068, SOL-USD:1.1080, IYR:0.3587, SOYB:0.5441
Covariance matrix (annualized):
[[0.048038, 0.094715, 0.031163, -0.014043], [0.094715, 0.85444, 0.025429, 0.005422], [0.031163, 0.025429, 0.034499, -0.019363], [-0.014043, 0.005422, -0.019363, 0.047083]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_IVV=0.0000, w_SOL-USD=0.0146, w_IYR=0.5016, w_SOYB=0.4838

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.0000, w_SOL-USD=0.0146, w_IYR=0.5016, w_SOYB=0.4838
Portfolio annualized return: 45.93%, volatility: 10.46%
Sharpe ratio: (0.4593 - 0.0400) / 0.1046 = 4.0102


4-asset optimization. Max-Sharpe: 2.493. Portfolio: return=68.28%, vol=25.78%. Weights: w_VTI=0.0000, w_SOL-USD=0.0808, w_WEAT=0.9192, w_HYG=0.0000.

Question:
Assets: VTI, SOL-USD, WEAT, HYG
Annualized mean returns: VTI:0.0931, SOL-USD:2.2239, WEAT:0.5472, HYG:-0.0460
Covariance matrix (annualized):
[[0.035013, 0.120367, 0.007882, 0.009015], [0.120367, 2.77279, 0.001855, 0.026887], [0.007882, 0.001855, 0.056904, 0.00502], [0.009015, 0.026887, 0.00502, 0.004114]]
Risk-free rate: 4.00%
Constraints: weights 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_SOL-USD=0.0808, w_WEAT=0.9192, w_HYG=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0000, w_SOL-USD=0.0808, w_WEAT=0.9192, w_HYG=0.0000
Portfolio annualized return: 68.28%, volatility: 25.78%
Sharpe ratio: (0.6828 - 0.0400) / 0.2578 = 2.4931


4-asset optimization. Max-Sharpe: 3.987. Portfolio: return=27.17%, vol=5.81%. Weights: w_XLE=0.1692, w_BNB-USD=0.0000, w_INDS=0.0000, w_CSHI=0.8308.

Question:
Assets: XLE, BNB-USD, INDS, CSHI
Annualized mean returns: XLE:1.3090, BNB-USD:0.6612, INDS:0.2706, CSHI:0.0605
Covariance matrix (annualized):
[[0.102708, 0.098383, 0.029584, 0.001348], [0.098383, 0.539629, 0.07588, 0.000308], [0.029584, 0.07588, 0.078089, 0.001013], [0.001348, 0.000308, 0.001013, 8.4e-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_XLE=0.1692, w_BNB-USD=0.0000, w_INDS=0.0000, w_CSHI=0.8308

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.1692, w_BNB-USD=0.0000, w_INDS=0.0000, w_CSHI=0.8308
Portfolio annualized return: 27.17%, volatility: 5.81%
Sharpe ratio: (0.2717 - 0.0400) / 0.0581 = 3.9870


4-asset optimization. Max-Sharpe: 4.373. Portfolio: return=227.20%, vol=51.04%. Weights: w_MTUM=0.1440, w_ETH-USD=0.8560, w_INDS=0.0000, w_BIL=0.0000.

Question:
Assets: MTUM, ETH-USD, INDS, BIL
Annualized mean returns: MTUM:0.3140, ETH-USD:2.6014, INDS:-0.0086, BIL:0.0002
Covariance matrix (annualized):
[[0.043526, 0.030039, 0.027545, -3.3e-05], [0.030039, 0.344187, 0.013338, -3e-05], [0.027545, 0.013338, 0.049622, -2.1e-05], [-3.3e-05, -3e-05, -2.1e-05, 1e-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_MTUM=0.1440, w_ETH-USD=0.8560, w_INDS=0.0000, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.1440, w_ETH-USD=0.8560, w_INDS=0.0000, w_BIL=0.0000
Portfolio annualized return: 227.20%, volatility: 51.04%
Sharpe ratio: (2.2720 - 0.0400) / 0.5104 = 4.3730


4-asset optimization. Max-Sharpe: 1.238. Portfolio: return=145.83%, vol=114.60%. Weights: w_EWJ=0.0000, w_LINK-USD=1.0000, w_UNG=0.0000, w_BIL=0.0000.

Question:
Assets: EWJ, LINK-USD, UNG, BIL
Annualized mean returns: EWJ:-0.1412, LINK-USD:1.4583, UNG:-0.4844, BIL:-0.0013
Covariance matrix (annualized):
[[0.02119, 0.030807, 0.004802, -6e-06], [0.030807, 1.313355, 0.032919, 6.1e-05], [0.004802, 0.032919, 0.081859, 7.7e-05], [-6e-06, 6.1e-05, 7.7e-05, 2e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_EWJ=0.0000, w_LINK-USD=1.0000, w_UNG=0.0000, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=0.0000, w_LINK-USD=1.0000, w_UNG=0.0000, w_BIL=0.0000
Portfolio annualized return: 145.83%, volatility: 114.60%
Sharpe ratio: (1.4583 - 0.0400) / 1.1460 = 1.2376


4-asset optimization. Max-Sharpe: 2.324. Portfolio: return=56.63%, vol=22.65%. Weights: w_VEA=1.0000, w_ETH-USD=0.0000, w_BIL=0.0000, w_DBA=0.0000.

Question:
Assets: VEA, ETH-USD, BIL, DBA
Annualized mean returns: VEA:0.5663, ETH-USD:0.5142, BIL:0.0277, DBA:-0.1067
Covariance matrix (annualized):
[[0.051288, 0.080315, -3.7e-05, 0.007601], [0.080315, 0.626151, -0.000547, 0.011627], [-3.7e-05, -0.000547, 8e-06, 3e-06], [0.007601, 0.011627, 3e-06, 0.008767]]
Risk-free rate: 4.00%
Constraints: weights 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=1.0000, w_ETH-USD=0.0000, w_BIL=0.0000, w_DBA=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VEA=1.0000, w_ETH-USD=0.0000, w_BIL=0.0000, w_DBA=0.0000
Portfolio annualized return: 56.63%, volatility: 22.65%
Sharpe ratio: (0.5663 - 0.0400) / 0.2265 = 2.3239


4-asset optimization. Max-Sharpe: -2.088. Portfolio: return=-308.78%, vol=149.81%. Weights: w_FXI=0.0000, w_LINK-USD=1.0000, w_ICSH=0.0000, w_IEF=0.0000.

Question:
Assets: FXI, LINK-USD, ICSH, IEF
Annualized mean returns: FXI:-0.2408, LINK-USD:-3.0878, ICSH:0.0101, IEF:-0.0861
Covariance matrix (annualized):
[[0.087382, 0.109566, 0.000127, -0.001031], [0.109566, 2.244393, 0.000557, -0.000713], [0.000127, 0.000557, 6.2e-05, -1.7e-05], [-0.001031, -0.000713, -1.7e-05, 0.002046]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_FXI=0.0000, w_LINK-USD=1.0000, w_ICSH=0.0000, w_IEF=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_FXI=0.0000, w_LINK-USD=1.0000, w_ICSH=0.0000, w_IEF=0.0000
Portfolio annualized return: -308.78%, volatility: 149.81%
Sharpe ratio: (-3.0878 - 0.0400) / 1.4981 = -2.0878


4-asset optimization. Max-Sharpe: 1.283. Portfolio: return=34.44%, vol=23.73%. Weights: w_^VIX=0.1791, w_LINK-USD=0.1281, w_SLV=0.6928, w_ITB=0.0000.

Question:
Assets: ^VIX, LINK-USD, SLV, ITB
Annualized mean returns: ^VIX:-0.0220, LINK-USD:0.3802, SLV:0.4324, ITB:-0.0100
Covariance matrix (annualized):
[[0.476624, -0.182299, -0.106038, -0.149443], [-0.182299, 0.39401, 0.0651, 0.087292], [-0.106038, 0.0651, 0.120163, 0.076757], [-0.149443, 0.087292, 0.076757, 0.150172]]
Risk-free rate: 4.00%
Constraints: weights 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=0.1791, w_LINK-USD=0.1281, w_SLV=0.6928, w_ITB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.1791, w_LINK-USD=0.1281, w_SLV=0.6928, w_ITB=0.0000
Portfolio annualized return: 34.44%, volatility: 23.73%
Sharpe ratio: (0.3444 - 0.0400) / 0.2373 = 1.2827


4-asset optimization. Max-Sharpe: 0.618. Portfolio: return=27.16%, vol=37.47%. Weights: w_XLB=0.0000, w_BNB-USD=1.0000, w_CSHI=0.0000, w_SCHP=0.0000.

Question:
Assets: XLB, BNB-USD, CSHI, SCHP
Annualized mean returns: XLB:-0.2035, BNB-USD:0.2716, CSHI:0.0407, SCHP:-0.4024
Covariance matrix (annualized):
[[0.092573, 0.061324, 0.002489, 0.01157], [0.061324, 0.140373, 0.001357, 0.010055], [0.002489, 0.001357, 0.000126, 0.000276], [0.01157, 0.010055, 0.000276, 0.006409]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLB=0.0000, w_BNB-USD=1.0000, w_CSHI=0.0000, w_SCHP=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0000, w_BNB-USD=1.0000, w_CSHI=0.0000, w_SCHP=0.0000
Portfolio annualized return: 27.16%, volatility: 37.47%
Sharpe ratio: (0.2716 - 0.0400) / 0.3747 = 0.6180


4-asset optimization. Max-Sharpe: -3.068. Portfolio: return=-372.95%, vol=122.88%. Weights: w_XLP=0.0000, w_ADA-USD=1.0000, w_INDS=0.0000, w_SLV=0.0000.

Question:
Assets: XLP, ADA-USD, INDS, SLV
Annualized mean returns: XLP:-0.3079, ADA-USD:-3.7295, INDS:-1.0291, SLV:-0.5565
Covariance matrix (annualized):
[[0.042954, 0.086514, 0.048306, 0.021093], [0.086514, 1.510047, 0.198738, 0.092805], [0.048306, 0.198738, 0.103739, 0.041608], [0.021093, 0.092805, 0.041608, 0.077128]]
Risk-free rate: 4.00%
Constraints: weights 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_ADA-USD=1.0000, w_INDS=0.0000, w_SLV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.0000, w_ADA-USD=1.0000, w_INDS=0.0000, w_SLV=0.0000
Portfolio annualized return: -372.95%, volatility: 122.88%
Sharpe ratio: (-3.7295 - 0.0400) / 1.2288 = -3.0675


4-asset optimization. Max-Sharpe: 4.208. Portfolio: return=44.64%, vol=9.66%. Weights: w_IVV=0.7028, w_BNB-USD=0.0000, w_BIL=0.0000, w_TLT=0.2972.

Question:
Assets: IVV, BNB-USD, BIL, TLT
Annualized mean returns: IVV:0.5932, BNB-USD:0.8557, BIL:-0.0006, TLT:0.0994
Covariance matrix (annualized):
[[0.019677, 0.044485, 2.1e-05, -0.003806], [0.044485, 0.395771, 9.9e-05, -0.002333], [2.1e-05, 9.9e-05, 1e-06, 2.2e-05], [-0.003806, -0.002333, 2.2e-05, 0.013593]]
Risk-free rate: 4.00%
Constraints: weights 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=0.7028, w_BNB-USD=0.0000, w_BIL=0.0000, w_TLT=0.2972

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.7028, w_BNB-USD=0.0000, w_BIL=0.0000, w_TLT=0.2972
Portfolio annualized return: 44.64%, volatility: 9.66%
Sharpe ratio: (0.4464 - 0.0400) / 0.0966 = 4.2077


4-asset optimization. Max-Sharpe: -0.099. Portfolio: return=-14.78%, vol=190.35%. Weights: w_XLRE=0.0000, w_XRP-USD=1.0000, w_VNQ=0.0000, w_TIP=0.0000.

Question:
Assets: XLRE, XRP-USD, VNQ, TIP
Annualized mean returns: XLRE:-0.4261, XRP-USD:-0.1478, VNQ:-0.6190, TIP:0.0007
Covariance matrix (annualized):
[[0.037949, 0.058347, 0.03705, 9.2e-05], [0.058347, 3.623302, 0.070722, 0.002215], [0.03705, 0.070722, 0.037372, 6.7e-05], [9.2e-05, 0.002215, 6.7e-05, 0.000104]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLRE=0.0000, w_XRP-USD=1.0000, w_VNQ=0.0000, w_TIP=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.0000, w_XRP-USD=1.0000, w_VNQ=0.0000, w_TIP=0.0000
Portfolio annualized return: -14.78%, volatility: 190.35%
Sharpe ratio: (-0.1478 - 0.0400) / 1.9035 = -0.0987


4-asset optimization. Max-Sharpe: 1.339. Portfolio: return=152.89%, vol=111.20%. Weights: w_EFA=0.0000, w_XRP-USD=1.0000, w_ITB=0.0000, w_PDBC=0.0000.

Question:
Assets: EFA, XRP-USD, ITB, PDBC
Annualized mean returns: EFA:0.0441, XRP-USD:1.5289, ITB:-0.1241, PDBC:0.0311
Covariance matrix (annualized):
[[0.010494, 0.041678, 0.012217, 0.008561], [0.041678, 1.236633, 0.090212, 0.026286], [0.012217, 0.090212, 0.045108, 0.013603], [0.008561, 0.026286, 0.013603, 0.034813]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_EFA=0.0000, w_XRP-USD=1.0000, w_ITB=0.0000, w_PDBC=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.0000, w_XRP-USD=1.0000, w_ITB=0.0000, w_PDBC=0.0000
Portfolio annualized return: 152.89%, volatility: 111.20%
Sharpe ratio: (1.5289 - 0.0400) / 1.1120 = 1.3389


4-asset optimization. Max-Sharpe: 0.414. Portfolio: return=14.10%, vol=24.38%. Weights: w_XLB=1.0000, w_ADA-USD=0.0000, w_BIL=0.0000, w_SCHP=0.0000.

Question:
Assets: XLB, ADA-USD, BIL, SCHP
Annualized mean returns: XLB:0.1410, ADA-USD:-0.3266, BIL:0.0000, SCHP:0.0236
Covariance matrix (annualized):
[[0.059418, 0.089565, 2.8e-05, 0.000522], [0.089565, 0.742697, 0.000228, 0.007792], [2.8e-05, 0.000228, 2e-06, 6e-06], [0.000522, 0.007792, 6e-06, 0.000696]]
Risk-free rate: 4.00%
Constraints: weights 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=1.0000, w_ADA-USD=0.0000, w_BIL=0.0000, w_SCHP=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=1.0000, w_ADA-USD=0.0000, w_BIL=0.0000, w_SCHP=0.0000
Portfolio annualized return: 14.10%, volatility: 24.38%
Sharpe ratio: (0.1410 - 0.0400) / 0.2438 = 0.4144


4-asset optimization. Max-Sharpe: 2.688. Portfolio: return=87.34%, vol=31.00%. Weights: w_EFA=0.0000, w_BNB-USD=0.0000, w_ICSH=0.0000, w_UNG=1.0000.

Question:
Assets: EFA, BNB-USD, ICSH, UNG
Annualized mean returns: EFA:-0.0506, BNB-USD:-2.6433, ICSH:0.0279, UNG:0.8734
Covariance matrix (annualized):
[[0.019017, 0.011096, -7.9e-05, 0.010466], [0.011096, 0.466423, 0.000569, 0.003044], [-7.9e-05, 0.000569, 1.2e-05, -0.000297], [0.010466, 0.003044, -0.000297, 0.096117]]
Risk-free rate: 4.00%
Constraints: weights 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_BNB-USD=0.0000, w_ICSH=0.0000, w_UNG=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.0000, w_BNB-USD=0.0000, w_ICSH=0.0000, w_UNG=1.0000
Portfolio annualized return: 87.34%, volatility: 31.00%
Sharpe ratio: (0.8734 - 0.0400) / 0.3100 = 2.6881


4-asset optimization. Max-Sharpe: 3.000. Portfolio: return=36.28%, vol=10.76%. Weights: w_EFA=0.8891, w_BTC-USD=0.1109, w_VCIT=0.0000, w_IYR=0.0000.

Question:
Assets: EFA, BTC-USD, VCIT, IYR
Annualized mean returns: EFA:0.2021, BTC-USD:1.6513, VCIT:0.0657, IYR:0.0858
Covariance matrix (annualized):
[[0.006938, -0.003189, 0.00088, 0.004196], [-0.003189, 0.546695, 0.006753, 0.014617], [0.00088, 0.006753, 0.001804, 0.002475], [0.004196, 0.014617, 0.002475, 0.015416]]
Risk-free rate: 4.00%
Constraints: weights 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=0.8891, w_BTC-USD=0.1109, w_VCIT=0.0000, w_IYR=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.8891, w_BTC-USD=0.1109, w_VCIT=0.0000, w_IYR=0.0000
Portfolio annualized return: 36.28%, volatility: 10.76%
Sharpe ratio: (0.3628 - 0.0400) / 0.1076 = 2.9997


4-asset optimization. Max-Sharpe: -2.055. Portfolio: return=-235.49%, vol=116.55%. Weights: w_EFA=0.0000, w_AVAX-USD=1.0000, w_HAUZ=0.0000, w_BIL=0.0000.

Question:
Assets: EFA, AVAX-USD, HAUZ, BIL
Annualized mean returns: EFA:-0.3300, AVAX-USD:-2.3549, HAUZ:-0.4682, BIL:0.0030
Covariance matrix (annualized):
[[0.048519, 0.097978, 0.038784, -3.3e-05], [0.097978, 1.358385, 0.079594, -0.000279], [0.038784, 0.079594, 0.035593, -2.9e-05], [-3.3e-05, -0.000279, -2.9e-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_EFA=0.0000, w_AVAX-USD=1.0000, w_HAUZ=0.0000, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EFA=0.0000, w_AVAX-USD=1.0000, w_HAUZ=0.0000, w_BIL=0.0000
Portfolio annualized return: -235.49%, volatility: 116.55%
Sharpe ratio: (-2.3549 - 0.0400) / 1.1655 = -2.0549


4-asset optimization. Max-Sharpe: 1.147. Portfolio: return=47.74%, vol=38.12%. Weights: w_XLI=0.0000, w_SOL-USD=0.0000, w_WEAT=1.0000, w_MORT=0.0000.

Question:
Assets: XLI, SOL-USD, WEAT, MORT
Annualized mean returns: XLI:-0.6491, SOL-USD:-0.5111, WEAT:0.4774, MORT:-1.7510
Covariance matrix (annualized):
[[0.065526, 0.076528, -0.003201, 0.065039], [0.076528, 0.404213, -0.032721, 0.044265], [-0.003201, -0.032721, 0.145328, 0.01046], [0.065039, 0.044265, 0.01046, 0.122629]]
Risk-free rate: 4.00%
Constraints: weights 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_SOL-USD=0.0000, w_WEAT=1.0000, w_MORT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.0000, w_SOL-USD=0.0000, w_WEAT=1.0000, w_MORT=0.0000
Portfolio annualized return: 47.74%, volatility: 38.12%
Sharpe ratio: (0.4774 - 0.0400) / 0.3812 = 1.1474


4-asset optimization. Max-Sharpe: 3.412. Portfolio: return=38.68%, vol=10.16%. Weights: w_QUAL=1.0000, w_DOT-USD=0.0000, w_SGOV=0.0000, w_ITB=0.0000.

Question:
Assets: QUAL, DOT-USD, SGOV, ITB
Annualized mean returns: QUAL:0.3868, DOT-USD:-1.0678, SGOV:-0.0001, ITB:0.3473
Covariance matrix (annualized):
[[0.010327, -0.002573, 1.8e-05, 0.013158], [-0.002573, 1.164386, -0.00015, 0.005791], [1.8e-05, -0.00015, 1e-06, 3e-06], [0.013158, 0.005791, 3e-06, 0.045957]]
Risk-free rate: 4.00%
Constraints: weights 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_DOT-USD=0.0000, w_SGOV=0.0000, w_ITB=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=1.0000, w_DOT-USD=0.0000, w_SGOV=0.0000, w_ITB=0.0000
Portfolio annualized return: 38.68%, volatility: 10.16%
Sharpe ratio: (0.3868 - 0.0400) / 0.1016 = 3.4122


4-asset optimization. Max-Sharpe: -1.159. Portfolio: return=-87.15%, vol=78.68%. Weights: w_EEM=0.0000, w_ADA-USD=1.0000, w_BIL=0.0000, w_HAUZ=0.0000.

Question:
Assets: EEM, ADA-USD, BIL, HAUZ
Annualized mean returns: EEM:-0.0640, ADA-USD:-0.8715, BIL:0.0224, HAUZ:-0.0381
Covariance matrix (annualized):
[[0.026028, -0.012452, 2.4e-05, 0.011684], [-0.012452, 0.619, 1.6e-05, -0.008779], [2.4e-05, 1.6e-05, 4e-06, 4.5e-05], [0.011684, -0.008779, 4.5e-05, 0.009573]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_EEM=0.0000, w_ADA-USD=1.0000, w_BIL=0.0000, w_HAUZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_ADA-USD=1.0000, w_BIL=0.0000, w_HAUZ=0.0000
Portfolio annualized return: -87.15%, volatility: 78.68%
Sharpe ratio: (-0.8715 - 0.0400) / 0.7868 = -1.1585


4-asset optimization. Max-Sharpe: 2.561. Portfolio: return=285.66%, vol=109.99%. Weights: w_XLRE=0.0000, w_XRP-USD=1.0000, w_SHY=0.0000, w_DBA=0.0000.

Question:
Assets: XLRE, XRP-USD, SHY, DBA
Annualized mean returns: XLRE:-0.6083, XRP-USD:2.8566, SHY:-0.0326, DBA:-0.1093
Covariance matrix (annualized):
[[0.082781, 0.028856, 0.00337, 0.005461], [0.028856, 1.209814, -0.000796, 0.029056], [0.00337, -0.000796, 0.000509, 0.000441], [0.005461, 0.029056, 0.000441, 0.011919]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLRE=0.0000, w_XRP-USD=1.0000, w_SHY=0.0000, w_DBA=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLRE=0.0000, w_XRP-USD=1.0000, w_SHY=0.0000, w_DBA=0.0000
Portfolio annualized return: 285.66%, volatility: 109.99%
Sharpe ratio: (2.8566 - 0.0400) / 1.0999 = 2.5607


4-asset optimization. Max-Sharpe: 5.714. Portfolio: return=185.50%, vol=31.77%. Weights: w_QUAL=0.8553, w_MATIC-USD=0.1447, w_SGOV=0.0000, w_SHV=0.0000.

Question:
Assets: QUAL, MATIC-USD, SGOV, SHV
Annualized mean returns: QUAL:0.2667, MATIC-USD:11.2446, SGOV:0.0003, SHV:0.0000
Covariance matrix (annualized):
[[0.018117, -0.01998, 0.0, -4.5e-05], [-0.01998, 4.423669, -0.000127, 0.000354], [0.0, -0.000127, 0.0, -0.0], [-4.5e-05, 0.000354, -0.0, 1e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QUAL=0.8553, w_MATIC-USD=0.1447, w_SGOV=0.0000, w_SHV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.8553, w_MATIC-USD=0.1447, w_SGOV=0.0000, w_SHV=0.0000
Portfolio annualized return: 185.50%, volatility: 31.77%
Sharpe ratio: (1.8550 - 0.0400) / 0.3177 = 5.7137


4-asset optimization. Max-Sharpe: 3.195. Portfolio: return=200.57%, vol=61.52%. Weights: w_EEM=0.0000, w_MATIC-USD=0.3885, w_DBB=0.0000, w_IYR=0.6115.

Question:
Assets: EEM, MATIC-USD, DBB, IYR
Annualized mean returns: EEM:-0.2187, MATIC-USD:4.5061, DBB:-0.7275, IYR:0.4171
Covariance matrix (annualized):
[[0.041611, 0.127691, 0.021212, 0.026874], [0.127691, 2.035679, 0.071249, 0.112727], [0.021212, 0.071249, 0.065493, 0.017366], [0.026874, 0.112727, 0.017366, 0.047093]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_EEM=0.0000, w_MATIC-USD=0.3885, w_DBB=0.0000, w_IYR=0.6115

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_MATIC-USD=0.3885, w_DBB=0.0000, w_IYR=0.6115
Portfolio annualized return: 200.57%, volatility: 61.52%
Sharpe ratio: (2.0057 - 0.0400) / 0.6152 = 3.1954


4-asset optimization. Max-Sharpe: 2.569. Portfolio: return=30.00%, vol=10.12%. Weights: w_IWM=0.0000, w_BTC-USD=0.0000, w_JNK=0.0000, w_INDS=1.0000.

Question:
Assets: IWM, BTC-USD, JNK, INDS
Annualized mean returns: IWM:0.0872, BTC-USD:-1.6849, JNK:0.0083, INDS:0.3000
Covariance matrix (annualized):
[[0.016527, 0.011237, 0.002883, 0.003622], [0.011237, 0.279983, 0.000736, -0.005333], [0.002883, 0.000736, 0.001019, 0.000339], [0.003622, -0.005333, 0.000339, 0.010246]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_IWM=0.0000, w_BTC-USD=0.0000, w_JNK=0.0000, w_INDS=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.0000, w_BTC-USD=0.0000, w_JNK=0.0000, w_INDS=1.0000
Portfolio annualized return: 30.00%, volatility: 10.12%
Sharpe ratio: (0.3000 - 0.0400) / 0.1012 = 2.5687


4-asset optimization. Max-Sharpe: 0.970. Portfolio: return=11.43%, vol=7.66%. Weights: w_EWJ=1.0000, w_BNB-USD=0.0000, w_IYR=0.0000, w_SHY=0.0000.

Question:
Assets: EWJ, BNB-USD, IYR, SHY
Annualized mean returns: EWJ:0.1143, BNB-USD:-1.9780, IYR:-0.0475, SHY:0.0076
Covariance matrix (annualized):
[[0.005875, -0.003872, -0.000864, -0.000262], [-0.003872, 0.303748, 0.020189, 0.000589], [-0.000864, 0.020189, 0.013527, 0.000477], [-0.000262, 0.000589, 0.000477, 8.4e-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_EWJ=1.0000, w_BNB-USD=0.0000, w_IYR=0.0000, w_SHY=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EWJ=1.0000, w_BNB-USD=0.0000, w_IYR=0.0000, w_SHY=0.0000
Portfolio annualized return: 11.43%, volatility: 7.66%
Sharpe ratio: (0.1143 - 0.0400) / 0.0766 = 0.9696


4-asset optimization. Max-Sharpe: 6.423. Portfolio: return=166.13%, vol=25.24%. Weights: w_XLU=0.0000, w_LINK-USD=0.2958, w_XHB=0.1501, w_TLH=0.5541.

Question:
Assets: XLU, LINK-USD, XHB, TLH
Annualized mean returns: XLU:-0.1149, LINK-USD:4.7483, XHB:1.3571, TLH:0.0956
Covariance matrix (annualized):
[[0.130153, 0.0622, 0.136561, -0.01848], [0.0622, 0.581636, 0.110507, -0.006467], [0.136561, 0.110507, 0.246588, -0.032377], [-0.01848, -0.006467, -0.032377, 0.016171]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLU=0.0000, w_LINK-USD=0.2958, w_XHB=0.1501, w_TLH=0.5541

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLU=0.0000, w_LINK-USD=0.2958, w_XHB=0.1501, w_TLH=0.5541
Portfolio annualized return: 166.13%, volatility: 25.24%
Sharpe ratio: (1.6613 - 0.0400) / 0.2524 = 6.4226


4-asset optimization. Max-Sharpe: 5.192. Portfolio: return=139.71%, vol=26.14%. Weights: w_XLB=0.0000, w_MATIC-USD=0.0907, w_MORT=0.0000, w_BNO=0.9093.

Question:
Assets: XLB, MATIC-USD, MORT, BNO
Annualized mean returns: XLB:0.0408, MATIC-USD:4.8189, MORT:0.2597, BNO:1.0557
Covariance matrix (annualized):
[[0.03779, 0.045085, 0.026445, 0.022675], [0.045085, 3.353876, 0.001519, -0.070096], [0.026445, 0.001519, 0.044705, 0.017596], [0.022675, -0.070096, 0.017596, 0.06323]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLB=0.0000, w_MATIC-USD=0.0907, w_MORT=0.0000, w_BNO=0.9093

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0000, w_MATIC-USD=0.0907, w_MORT=0.0000, w_BNO=0.9093
Portfolio annualized return: 139.71%, volatility: 26.14%
Sharpe ratio: (1.3971 - 0.0400) / 0.2614 = 5.1921


4-asset optimization. Max-Sharpe: 5.731. Portfolio: return=61.72%, vol=10.07%. Weights: w_XLV=0.6251, w_AVAX-USD=0.0024, w_BIL=0.0000, w_UNG=0.3725.

Question:
Assets: XLV, AVAX-USD, BIL, UNG
Annualized mean returns: XLV:0.3035, AVAX-USD:0.0870, BIL:-0.0007, UNG:1.1470
Covariance matrix (annualized):
[[0.012635, 0.004819, 1.2e-05, -0.008804], [0.004819, 2.735375, 0.000112, -0.023291], [1.2e-05, 0.000112, 2e-06, 3.7e-05], [-0.008804, -0.023291, 3.7e-05, 0.067139]]
Risk-free rate: 4.00%
Constraints: weights 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=0.6251, w_AVAX-USD=0.0024, w_BIL=0.0000, w_UNG=0.3725

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.6251, w_AVAX-USD=0.0024, w_BIL=0.0000, w_UNG=0.3725
Portfolio annualized return: 61.72%, volatility: 10.07%
Sharpe ratio: (0.6172 - 0.0400) / 0.1007 = 5.7310


4-asset optimization. Max-Sharpe: 0.867. Portfolio: return=15.08%, vol=12.78%. Weights: w_ACWI=0.9597, w_SOL-USD=0.0403, w_TLH=0.0000, w_BIL=0.0000.

Question:
Assets: ACWI, SOL-USD, TLH, BIL
Annualized mean returns: ACWI:0.1442, SOL-USD:0.3092, TLH:0.0371, BIL:-0.0013
Covariance matrix (annualized):
[[0.015608, 0.009451, 0.002412, 2.3e-05], [0.009451, 0.759903, 0.005981, 0.000293], [0.002412, 0.005981, 0.00687, 3.2e-05], [2.3e-05, 0.000293, 3.2e-05, 2e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_ACWI=0.9597, w_SOL-USD=0.0403, w_TLH=0.0000, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=0.9597, w_SOL-USD=0.0403, w_TLH=0.0000, w_BIL=0.0000
Portfolio annualized return: 15.08%, volatility: 12.78%
Sharpe ratio: (0.1508 - 0.0400) / 0.1278 = 0.8668


4-asset optimization. Max-Sharpe: 2.031. Portfolio: return=78.86%, vol=36.86%. Weights: w_XLB=0.6746, w_SOL-USD=0.3254, w_TLT=0.0000, w_VNQI=0.0000.

Question:
Assets: XLB, SOL-USD, TLT, VNQI
Annualized mean returns: XLB:0.3438, SOL-USD:1.7107, TLT:-0.6834, VNQI:-0.2800
Covariance matrix (annualized):
[[0.051587, 0.06251, -0.004946, 0.02932], [0.06251, 0.802252, 0.055228, 0.050316], [-0.004946, 0.055228, 0.038965, -0.002511], [0.02932, 0.050316, -0.002511, 0.030215]]
Risk-free rate: 4.00%
Constraints: weights 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=0.6746, w_SOL-USD=0.3254, w_TLT=0.0000, w_VNQI=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.6746, w_SOL-USD=0.3254, w_TLT=0.0000, w_VNQI=0.0000
Portfolio annualized return: 78.86%, volatility: 36.86%
Sharpe ratio: (0.7886 - 0.0400) / 0.3686 = 2.0309


4-asset optimization. Max-Sharpe: 2.375. Portfolio: return=36.70%, vol=13.77%. Weights: w_XLF=0.0000, w_XRP-USD=0.0485, w_DBC=0.0000, w_XHB=0.9515.

Question:
Assets: XLF, XRP-USD, DBC, XHB
Annualized mean returns: XLF:0.1776, XRP-USD:0.7274, DBC:-0.3592, XHB:0.3486
Covariance matrix (annualized):
[[0.018162, 0.002507, 0.005378, 0.010616], [0.002507, 0.438831, 0.012829, 0.019528], [0.005378, 0.012829, 0.01548, 0.002173], [0.010616, 0.019528, 0.002173, 0.017814]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLF=0.0000, w_XRP-USD=0.0485, w_DBC=0.0000, w_XHB=0.9515

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.0000, w_XRP-USD=0.0485, w_DBC=0.0000, w_XHB=0.9515
Portfolio annualized return: 36.70%, volatility: 13.77%
Sharpe ratio: (0.3670 - 0.0400) / 0.1377 = 2.3746


4-asset optimization. Max-Sharpe: 2.531. Portfolio: return=39.95%, vol=14.21%. Weights: w_IWM=0.4597, w_ADA-USD=0.0000, w_TLH=0.5403, w_SGOV=0.0000.

Question:
Assets: IWM, ADA-USD, TLH, SGOV
Annualized mean returns: IWM:0.5313, ADA-USD:-0.1963, TLH:0.2874, SGOV:0.0135
Covariance matrix (annualized):
[[0.06259, 0.104799, -0.002204, -8.2e-05], [0.104799, 0.536535, -0.007335, -7.6e-05], [-0.002204, -0.007335, 0.027575, 3.9e-05], [-8.2e-05, -7.6e-05, 3.9e-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_IWM=0.4597, w_ADA-USD=0.0000, w_TLH=0.5403, w_SGOV=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IWM=0.4597, w_ADA-USD=0.0000, w_TLH=0.5403, w_SGOV=0.0000
Portfolio annualized return: 39.95%, volatility: 14.21%
Sharpe ratio: (0.3995 - 0.0400) / 0.1421 = 2.5307


4-asset optimization. Max-Sharpe: 4.602. Portfolio: return=454.95%, vol=97.98%. Weights: w_XLP=0.0000, w_MATIC-USD=1.0000, w_XHB=0.0000, w_HYG=0.0000.

Question:
Assets: XLP, MATIC-USD, XHB, HYG
Annualized mean returns: XLP:-0.3984, MATIC-USD:4.5495, XHB:-0.4376, HYG:-0.1821
Covariance matrix (annualized):
[[0.032755, 0.043926, 0.04999, 0.014588], [0.043926, 0.960019, 0.087176, 0.019061], [0.04999, 0.087176, 0.094586, 0.025407], [0.014588, 0.019061, 0.025407, 0.009851]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLP=0.0000, w_MATIC-USD=1.0000, w_XHB=0.0000, w_HYG=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLP=0.0000, w_MATIC-USD=1.0000, w_XHB=0.0000, w_HYG=0.0000
Portfolio annualized return: 454.95%, volatility: 97.98%
Sharpe ratio: (4.5495 - 0.0400) / 0.9798 = 4.6025


4-asset optimization. Max-Sharpe: 8.386. Portfolio: return=81.48%, vol=9.24%. Weights: w_MTUM=0.1771, w_ETH-USD=0.0408, w_UNG=0.0000, w_IYR=0.7821.

Question:
Assets: MTUM, ETH-USD, UNG, IYR
Annualized mean returns: MTUM:0.7663, ETH-USD:-0.0536, UNG:-1.1399, IYR:0.8710
Covariance matrix (annualized):
[[0.024049, -0.007795, 0.008548, 0.005191], [-0.007795, 0.791109, 0.066059, -0.040799], [0.008548, 0.066059, 0.255287, -0.002017], [0.005191, -0.040799, -0.002017, 0.012657]]
Risk-free rate: 4.00%
Constraints: weights 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=0.1771, w_ETH-USD=0.0408, w_UNG=0.0000, w_IYR=0.7821

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_MTUM=0.1771, w_ETH-USD=0.0408, w_UNG=0.0000, w_IYR=0.7821
Portfolio annualized return: 81.48%, volatility: 9.24%
Sharpe ratio: (0.8148 - 0.0400) / 0.0924 = 8.3863


4-asset optimization. Max-Sharpe: 0.043. Portfolio: return=6.51%, vol=57.98%. Weights: w_XLV=0.0000, w_BTC-USD=1.0000, w_STIP=0.0000, w_BIL=0.0000.

Question:
Assets: XLV, BTC-USD, STIP, BIL
Annualized mean returns: XLV:-0.0729, BTC-USD:0.0651, STIP:0.0397, BIL:0.0227
Covariance matrix (annualized):
[[0.0398, -0.027619, 0.000201, -1.6e-05], [-0.027619, 0.336167, -0.00111, -0.000177], [0.000201, -0.00111, 0.00027, 1e-05], [-1.6e-05, -0.000177, 1e-05, 4e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLV=0.0000, w_BTC-USD=1.0000, w_STIP=0.0000, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0000, w_BTC-USD=1.0000, w_STIP=0.0000, w_BIL=0.0000
Portfolio annualized return: 6.51%, volatility: 57.98%
Sharpe ratio: (0.0651 - 0.0400) / 0.5798 = 0.0433


4-asset optimization. Max-Sharpe: 3.914. Portfolio: return=63.73%, vol=15.26%. Weights: w_IVV=0.8428, w_BNB-USD=0.1572, w_XHB=0.0000, w_BIL=0.0000.

Question:
Assets: IVV, BNB-USD, XHB, BIL
Annualized mean returns: IVV:0.3133, BNB-USD:2.3749, XHB:0.3950, BIL:-0.0020
Covariance matrix (annualized):
[[0.009306, 0.017881, 0.01448, -2e-06], [0.017881, 0.483332, 0.028238, -9e-05], [0.01448, 0.028238, 0.047675, -2.2e-05], [-2e-06, -9e-05, -2.2e-05, 2e-06]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_IVV=0.8428, w_BNB-USD=0.1572, w_XHB=0.0000, w_BIL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_IVV=0.8428, w_BNB-USD=0.1572, w_XHB=0.0000, w_BIL=0.0000
Portfolio annualized return: 63.73%, volatility: 15.26%
Sharpe ratio: (0.6373 - 0.0400) / 0.1526 = 3.9140


4-asset optimization. Max-Sharpe: 4.651. Portfolio: return=70.19%, vol=14.23%. Weights: w_XLB=0.0777, w_ADA-USD=0.0000, w_STIP=0.0000, w_CORN=0.9223.

Question:
Assets: XLB, ADA-USD, STIP, CORN
Annualized mean returns: XLB:0.3449, ADA-USD:-1.3298, STIP:0.0317, CORN:0.7320
Covariance matrix (annualized):
[[0.057546, 0.097111, 0.001215, 0.005268], [0.097111, 0.812388, 0.004277, 0.007587], [0.001215, 0.004277, 0.000151, 0.000355], [0.005268, 0.007587, 0.000355, 0.022512]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0777, w_ADA-USD=0.0000, w_STIP=0.0000, w_CORN=0.9223

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLB=0.0777, w_ADA-USD=0.0000, w_STIP=0.0000, w_CORN=0.9223
Portfolio annualized return: 70.19%, volatility: 14.23%
Sharpe ratio: (0.7019 - 0.0400) / 0.1423 = 4.6510