Question:
Assets: IVV, UNG
IVV: annualized_mean_return=0.6552, daily_std=0.0110
UNG: annualized_mean_return=-0.4284, daily_std=0.0333
Minimum required portfolio return (annualized): 0.2769
Market regime: sideways

Compute portfolio weights (w_IVV, w_UNG) 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_UNG=X.XXXX

Answer: w_IVV=0.8983, w_UNG=0.1017

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.001112 - -0.000006) / (0.000121 + 0.001112 - -0.000012)
  Unconstrained: w_IVV=0.8984
  After long-only clamp: w_IVV=0.8984, w_UNG=0.1016.


Question:
Assets: EEM, SCHH
EEM: annualized_mean_return=0.5292, daily_std=0.0081
SCHH: annualized_mean_return=0.0756, daily_std=0.0086
Minimum required portfolio return (annualized): 0.1800
Market regime: bull

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

Answer: w_EEM=0.5380, w_SCHH=0.4620

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000074 - 0.000018) / (0.000066 + 0.000074 - 0.000036)
  Unconstrained: w_EEM=0.5380
  After long-only clamp: w_EEM=0.5380, w_SCHH=0.4620.


ETH-USD σ=0.0447, VLUE σ=0.0112, ρ=0.176. Min-variance weights: ETH-USD=0.019, VLUE=0.981.

Question:
Assets: ETH-USD, VLUE
ETH-USD: annualized_mean_return=-2.1420, daily_std=0.0447
VLUE: annualized_mean_return=-0.2772, daily_std=0.0112
Minimum required portfolio return (annualized): -0.2857
Market regime: bear

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

Answer: w_ETH-USD=0.0046, w_VLUE=0.9954

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000126 - 0.000088) / (0.001994 + 0.000126 - 0.000176)
  Unconstrained: w_ETH-USD=0.0194
  After long-only clamp: w_ETH-USD=0.0194, w_VLUE=0.9806.


Question:
Assets: MTUM, SGOV
MTUM: annualized_mean_return=0.3276, daily_std=0.0068
SGOV: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0505
Market regime: bull

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

Answer: w_MTUM=0.0006, w_SGOV=0.9994

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000046 + 0.000000 - -0.000000)
  Unconstrained: w_MTUM=0.0015
  After long-only clamp: w_MTUM=0.0015, w_SGOV=0.9985.


Question:
Assets: AVAX-USD, FXI
AVAX-USD: annualized_mean_return=-2.0412, daily_std=0.0461
FXI: annualized_mean_return=0.1008, daily_std=0.0125
Minimum required portfolio return (annualized): 0.0068
Market regime: sideways

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

Answer: w_AVAX-USD=0.0439, w_FXI=0.9561

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000156 - -0.000096) / (0.002123 + 0.000156 - -0.000192)
  Unconstrained: w_AVAX-USD=0.1021
  After long-only clamp: w_AVAX-USD=0.1021, w_FXI=0.8979.


Question:
Assets: FXI, CSHI
FXI: annualized_mean_return=-0.1008, daily_std=0.0179
CSHI: annualized_mean_return=0.0756, daily_std=0.0004
Minimum required portfolio return (annualized): 0.0070
Market regime: sideways

Compute portfolio weights (w_FXI, w_CSHI) 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_CSHI=X.XXXX

Answer: w_FXI=0.0000, w_CSHI=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.000320 + 0.000000 - 0.000002)
  Unconstrained: w_FXI=-0.0022
  After long-only clamp: w_FXI=0.0000, w_CSHI=1.0000.


Question:
Assets: BNB-USD, BIL
BNB-USD: annualized_mean_return=0.3780, daily_std=0.0306
BIL: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0504
Market regime: sideways

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

Answer: w_BNB-USD=0.0000, w_BIL=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000933 + 0.000000 - 0.000000)
  Unconstrained: w_BNB-USD=-0.0001
  After long-only clamp: w_BNB-USD=0.0000, w_BIL=1.0000.


Question:
Assets: XLF, CSHI
XLF: annualized_mean_return=-0.1764, daily_std=0.0135
CSHI: annualized_mean_return=-0.0504, daily_std=0.0032
Minimum required portfolio return (annualized): -0.1228
Market regime: bear

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

Answer: w_XLF=0.0653, w_CSHI=0.9347

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000010 - -0.000003) / (0.000183 + 0.000010 - -0.000006)
  Unconstrained: w_XLF=0.0644
  After long-only clamp: w_XLF=0.0644, w_CSHI=0.9356.


Question:
Assets: XRP-USD, VNQ
XRP-USD: annualized_mean_return=7.1064, daily_std=0.0742
VNQ: annualized_mean_return=-0.2016, daily_std=0.0101
Minimum required portfolio return (annualized): 5.5237
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_VNQ) 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_VNQ=X.XXXX

Answer: w_XRP-USD=0.7834, w_VNQ=0.2166

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000101 - -0.000013) / (0.005508 + 0.000101 - -0.000025)
  Unconstrained: w_XRP-USD=0.0202
  After long-only clamp: w_XRP-USD=0.0202, w_VNQ=0.9798.


Question:
Assets: XLRE, GLD
XLRE: annualized_mean_return=-0.0504, daily_std=0.0106
GLD: annualized_mean_return=0.2520, daily_std=0.0087
Minimum required portfolio return (annualized): 0.0436
Market regime: sideways

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

Answer: w_XLRE=0.3629, w_GLD=0.6371

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000075 - 0.000026) / (0.000113 + 0.000075 - 0.000052)
  Unconstrained: w_XLRE=0.3632
  After long-only clamp: w_XLRE=0.3632, w_GLD=0.6368.


ETH-USD σ=0.0313, SGOV σ=0.0001, ρ=0.003. Min-variance weights: ETH-USD=0.000, SGOV=1.000.

Question:
Assets: ETH-USD, SGOV
ETH-USD: annualized_mean_return=-0.7308, daily_std=0.0313
SGOV: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): -0.2367
Market regime: sideways

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

Answer: w_ETH-USD=0.0000, w_SGOV=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000978 + 0.000000 - 0.000000)
  Unconstrained: w_ETH-USD=0.0000
  After long-only clamp: w_ETH-USD=0.0000, w_SGOV=1.0000.


LINK-USD σ=0.0493, CPER σ=0.0114, ρ=0.049. Min-variance weights: LINK-USD=0.041, CPER=0.959.

Question:
Assets: LINK-USD, CPER
LINK-USD: annualized_mean_return=-1.4364, daily_std=0.0493
CPER: annualized_mean_return=0.4788, daily_std=0.0114
Minimum required portfolio return (annualized): 0.2553
Market regime: sideways

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

Answer: w_LINK-USD=0.0412, w_CPER=0.9588

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000130 - 0.000027) / (0.002434 + 0.000130 - 0.000055)
  Unconstrained: w_LINK-USD=0.0411
  After long-only clamp: w_LINK-USD=0.0411, w_CPER=0.9589.


Question:
Assets: MTUM, SGOV
MTUM: annualized_mean_return=0.1764, daily_std=0.0076
SGOV: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.1459
Market regime: bull

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

Answer: w_MTUM=0.7579, w_SGOV=0.2421

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000058 + 0.000000 - 0.000000)
  Unconstrained: w_MTUM=-0.0035
  After long-only clamp: w_MTUM=0.0000, w_SGOV=1.0000.


Question:
Assets: VTI, IEF
VTI: annualized_mean_return=0.1764, daily_std=0.0067
IEF: annualized_mean_return=0.1260, daily_std=0.0030
Minimum required portfolio return (annualized): 0.1307
Market regime: sideways

Compute portfolio weights (w_VTI, w_IEF) 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_IEF=X.XXXX

Answer: w_VTI=0.1882, w_IEF=0.8118

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000009 - -0.000002) / (0.000045 + 0.000009 - -0.000004)
  Unconstrained: w_VTI=0.1863
  After long-only clamp: w_VTI=0.1863, w_IEF=0.8137.


Question:
Assets: BTC-USD, UNG
BTC-USD: annualized_mean_return=0.3780, daily_std=0.0242
UNG: annualized_mean_return=0.5796, daily_std=0.0482
Minimum required portfolio return (annualized): 0.3973
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_UNG) 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_UNG=X.XXXX

Answer: w_BTC-USD=0.8630, w_UNG=0.1370

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.002326 - 0.000260) / (0.000588 + 0.002326 - 0.000519)
  Unconstrained: w_BTC-USD=0.8629
  After long-only clamp: w_BTC-USD=0.8629, w_UNG=0.1371.


Question:
Assets: XLP, BNDX
XLP: annualized_mean_return=-0.0252, daily_std=0.0071
BNDX: annualized_mean_return=0.1260, daily_std=0.0019
Minimum required portfolio return (annualized): 0.1202
Market regime: bull

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

Answer: w_XLP=0.0384, w_BNDX=0.9616

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000004 - -0.000002) / (0.000051 + 0.000004 - -0.000004)
  Unconstrained: w_XLP=0.0945
  After long-only clamp: w_XLP=0.0945, w_BNDX=0.9055.


Question:
Assets: IWM, XHB
IWM: annualized_mean_return=0.5040, daily_std=0.0114
XHB: annualized_mean_return=0.6804, daily_std=0.0177
Minimum required portfolio return (annualized): 0.5040
Market regime: bull

Compute portfolio weights (w_IWM, w_XHB) 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_XHB=X.XXXX

Answer: w_IWM=1.0000, w_XHB=0.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000313 - 0.000143) / (0.000130 + 0.000313 - 0.000287)
  Unconstrained: w_IWM=1.0825
  After long-only clamp: w_IWM=1.0000, w_XHB=0.0000.


Question:
Assets: XLI, VNQI
XLI: annualized_mean_return=0.1512, daily_std=0.0070
VNQI: annualized_mean_return=0.0756, daily_std=0.0067
Minimum required portfolio return (annualized): 0.1426
Market regime: bull

Compute portfolio weights (w_XLI, w_VNQI) 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_VNQI=X.XXXX

Answer: w_XLI=0.8862, w_VNQI=0.1138

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000045 - 0.000021) / (0.000049 + 0.000045 - 0.000042)
  Unconstrained: w_XLI=0.4634
  After long-only clamp: w_XLI=0.4634, w_VNQI=0.5366.


Question:
Assets: FXI, SGOV
FXI: annualized_mean_return=0.4284, daily_std=0.0200
SGOV: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.2788
Market regime: sideways

Compute portfolio weights (w_FXI, w_SGOV) 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_SGOV=X.XXXX

Answer: w_FXI=0.6042, w_SGOV=0.3958

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000399 + 0.000000 - 0.000001)
  Unconstrained: w_FXI=-0.0008
  After long-only clamp: w_FXI=0.0000, w_SGOV=1.0000.


Question:
Assets: XLI, SCHH
XLI: annualized_mean_return=0.0504, daily_std=0.0079
SCHH: annualized_mean_return=0.0000, daily_std=0.0081
Minimum required portfolio return (annualized): 0.0157
Market regime: sideways

Compute portfolio weights (w_XLI, w_SCHH) 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_SCHH=X.XXXX

Answer: w_XLI=0.5195, w_SCHH=0.4805

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000066 - 0.000026) / (0.000063 + 0.000066 - 0.000053)
  Unconstrained: w_XLI=0.5197
  After long-only clamp: w_XLI=0.5197, w_SCHH=0.4803.


BTC-USD σ=0.0226, WEAT σ=0.0112, ρ=0.080. Min-variance weights: BTC-USD=0.176, WEAT=0.824.

Question:
Assets: BTC-USD, WEAT
BTC-USD: annualized_mean_return=-1.3356, daily_std=0.0226
WEAT: annualized_mean_return=0.0504, daily_std=0.0112
Minimum required portfolio return (annualized): -0.5615
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_WEAT) 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_WEAT=X.XXXX

Answer: w_BTC-USD=0.1764, w_WEAT=0.8236

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000125 - 0.000020) / (0.000509 + 0.000125 - 0.000040)
  Unconstrained: w_BTC-USD=0.1762
  After long-only clamp: w_BTC-USD=0.1762, w_WEAT=0.8238.


SOL-USD σ=0.0641, ICSH σ=0.0003, ρ=0.004. Min-variance weights: SOL-USD=0.000, ICSH=1.000.

Question:
Assets: SOL-USD, ICSH
SOL-USD: annualized_mean_return=-1.1844, daily_std=0.0641
ICSH: annualized_mean_return=0.0504, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0504
Market regime: sideways

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

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

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.004115 + 0.000000 - 0.000000)
  Unconstrained: w_SOL-USD=-0.0000
  After long-only clamp: w_SOL-USD=0.0000, w_ICSH=1.0000.


Question:
Assets: BTC-USD, UNG
BTC-USD: annualized_mean_return=0.2520, daily_std=0.0160
UNG: annualized_mean_return=-0.4032, daily_std=0.0339
Minimum required portfolio return (annualized): 0.0242
Market regime: bull

Compute portfolio weights (w_BTC-USD, w_UNG) 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_UNG=X.XXXX

Answer: w_BTC-USD=0.8635, w_UNG=0.1365

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.001151 - 0.000088) / (0.000256 + 0.001151 - 0.000177)
  Unconstrained: w_BTC-USD=0.8637
  After long-only clamp: w_BTC-USD=0.8637, w_UNG=0.1363.


Question:
Assets: XLB, CPER
XLB: annualized_mean_return=-0.2520, daily_std=0.0095
CPER: annualized_mean_return=0.3780, daily_std=0.0141
Minimum required portfolio return (annualized): 0.1099
Market regime: sideways

Compute portfolio weights (w_XLB, w_CPER) 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_CPER=X.XXXX

Answer: w_XLB=0.4256, w_CPER=0.5744

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000198 - 0.000016) / (0.000090 + 0.000198 - 0.000032)
  Unconstrained: w_XLB=0.7125
  After long-only clamp: w_XLB=0.7125, w_CPER=0.2875.


VTI σ=0.0074, AVAX-USD σ=0.0468, ρ=0.043. Min-variance weights: VTI=0.982, AVAX-USD=0.018.

Question:
Assets: VTI, AVAX-USD
VTI: annualized_mean_return=0.1008, daily_std=0.0074
AVAX-USD: annualized_mean_return=-2.7972, daily_std=0.0468
Minimum required portfolio return (annualized): -0.4849
Market regime: sideways

Compute portfolio weights (w_VTI, w_AVAX-USD) 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_AVAX-USD=X.XXXX

Answer: w_VTI=0.9821, w_AVAX-USD=0.0179

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.002186 - 0.000015) / (0.000054 + 0.002186 - 0.000030)
  Unconstrained: w_VTI=0.9821
  After long-only clamp: w_VTI=0.9821, w_AVAX-USD=0.0179.


Question:
Assets: VLUE, IEF
VLUE: annualized_mean_return=0.6300, daily_std=0.0095
IEF: annualized_mean_return=0.0504, daily_std=0.0037
Minimum required portfolio return (annualized): 0.4533
Market regime: bull

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

Answer: w_VLUE=0.6951, w_IEF=0.3049

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000014 - -0.000003) / (0.000090 + 0.000014 - -0.000005)
  Unconstrained: w_VLUE=0.1521
  After long-only clamp: w_VLUE=0.1521, w_IEF=0.8479.


Question:
Assets: DOT-USD, XHB
DOT-USD: annualized_mean_return=-0.3528, daily_std=0.0344
XHB: annualized_mean_return=0.6300, daily_std=0.0172
Minimum required portfolio return (annualized): 0.3482
Market regime: bull

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

Answer: w_DOT-USD=0.2459, w_XHB=0.7541

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000295 - -0.000136) / (0.001185 + 0.000295 - -0.000272)
  Unconstrained: w_DOT-USD=0.2459
  After long-only clamp: w_DOT-USD=0.2459, w_XHB=0.7541.


Question:
Assets: VTI, CSHI
VTI: annualized_mean_return=0.4032, daily_std=0.0065
CSHI: annualized_mean_return=0.0504, daily_std=0.0006
Minimum required portfolio return (annualized): 0.1556
Market regime: bull

Compute portfolio weights (w_VTI, w_CSHI) 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_CSHI=X.XXXX

Answer: w_VTI=0.2982, w_CSHI=0.7018

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000043 + 0.000000 - -0.000000)
  Unconstrained: w_VTI=0.0128
  After long-only clamp: w_VTI=0.0128, w_CSHI=0.9872.


Question:
Assets: XLB, BNDX
XLB: annualized_mean_return=0.2520, daily_std=0.0101
BNDX: annualized_mean_return=0.1008, daily_std=0.0019
Minimum required portfolio return (annualized): 0.1992
Market regime: bull

Compute portfolio weights (w_XLB, w_BNDX) 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_BNDX=X.XXXX

Answer: w_XLB=0.6508, w_BNDX=0.3492

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000004 - -0.000002) / (0.000102 + 0.000004 - -0.000005)
  Unconstrained: w_XLB=0.0563
  After long-only clamp: w_XLB=0.0563, w_BNDX=0.9437.


Question:
Assets: VTI, PDBC
VTI: annualized_mean_return=0.1512, daily_std=0.0083
PDBC: annualized_mean_return=0.2268, daily_std=0.0082
Minimum required portfolio return (annualized): 0.2115
Market regime: sideways

Compute portfolio weights (w_VTI, w_PDBC) 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_PDBC=X.XXXX

Answer: w_VTI=0.2024, w_PDBC=0.7976

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000068 - 0.000014) / (0.000068 + 0.000068 - 0.000027)
  Unconstrained: w_VTI=0.4966
  After long-only clamp: w_VTI=0.4966, w_PDBC=0.5034.


Question:
Assets: VTI, VNQI
VTI: annualized_mean_return=0.1512, daily_std=0.0082
VNQI: annualized_mean_return=-0.3780, daily_std=0.0079
Minimum required portfolio return (annualized): -0.2678
Market regime: sideways

Compute portfolio weights (w_VTI, w_VNQI) 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_VNQI=X.XXXX

Answer: w_VTI=0.4694, w_VNQI=0.5306

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000062 - 0.000024) / (0.000067 + 0.000062 - 0.000048)
  Unconstrained: w_VTI=0.4692
  After long-only clamp: w_VTI=0.4692, w_VNQI=0.5308.


Question:
Assets: VTI, BIL
VTI: annualized_mean_return=0.1512, daily_std=0.0083
BIL: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0949
Market regime: sideways

Compute portfolio weights (w_VTI, w_BIL) 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_BIL=X.XXXX

Answer: w_VTI=0.4415, w_BIL=0.5585

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000068 + 0.000000 - -0.000000)
  Unconstrained: w_VTI=0.0003
  After long-only clamp: w_VTI=0.0003, w_BIL=0.9997.


Question:
Assets: XLF, XHB
XLF: annualized_mean_return=0.0504, daily_std=0.0088
XHB: annualized_mean_return=-0.1512, daily_std=0.0145
Minimum required portfolio return (annualized): -0.0489
Market regime: sideways

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

Answer: w_XLF=1.0000, w_XHB=0.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000211 - 0.000080) / (0.000077 + 0.000211 - 0.000161)
  Unconstrained: w_XLF=1.0219
  After long-only clamp: w_XLF=1.0000, w_XHB=0.0000.


LINK-USD σ=0.0487, IGOV σ=0.0040, ρ=0.139. Min-variance weights: LINK-USD=0.000, IGOV=1.000.

Question:
Assets: LINK-USD, IGOV
LINK-USD: annualized_mean_return=-1.9152, daily_std=0.0487
IGOV: annualized_mean_return=0.0252, daily_std=0.0040
Minimum required portfolio return (annualized): -0.4187
Market regime: sideways

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

Answer: w_LINK-USD=0.0000, w_IGOV=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000016 - 0.000027) / (0.002371 + 0.000016 - 0.000054)
  Unconstrained: w_LINK-USD=-0.0047
  After long-only clamp: w_LINK-USD=0.0000, w_IGOV=1.0000.


AVAX-USD σ=0.0591, MORT σ=0.0144, ρ=0.197. Min-variance weights: AVAX-USD=0.012, MORT=0.988.

Question:
Assets: AVAX-USD, MORT
AVAX-USD: annualized_mean_return=-0.7560, daily_std=0.0591
MORT: annualized_mean_return=-0.0756, daily_std=0.0144
Minimum required portfolio return (annualized): -0.0786
Market regime: bear

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

Answer: w_AVAX-USD=0.0044, w_MORT=0.9956

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000208 - 0.000168) / (0.003496 + 0.000208 - 0.000336)
  Unconstrained: w_AVAX-USD=0.0120
  After long-only clamp: w_AVAX-USD=0.0120, w_MORT=0.9880.


Question:
Assets: QQQ, PALL
QQQ: annualized_mean_return=0.3780, daily_std=0.0069
PALL: annualized_mean_return=0.3528, daily_std=0.0211
Minimum required portfolio return (annualized): 0.3740
Market regime: bull

Compute portfolio weights (w_QQQ, w_PALL) 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_PALL=X.XXXX

Answer: w_QQQ=0.9097, w_PALL=0.0903

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000447 - 0.000004) / (0.000048 + 0.000447 - 0.000008)
  Unconstrained: w_QQQ=0.9097
  After long-only clamp: w_QQQ=0.9097, w_PALL=0.0903.


Question:
Assets: XLB, CPER
XLB: annualized_mean_return=0.1008, daily_std=0.0097
CPER: annualized_mean_return=0.5796, daily_std=0.0160
Minimum required portfolio return (annualized): 0.3948
Market regime: bull

Compute portfolio weights (w_XLB, w_CPER) 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_CPER=X.XXXX

Answer: w_XLB=0.3860, w_CPER=0.6140

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000255 - 0.000050) / (0.000094 + 0.000255 - 0.000100)
  Unconstrained: w_XLB=0.8239
  After long-only clamp: w_XLB=0.8239, w_CPER=0.1761.


Question:
Assets: EWJ, TIP
EWJ: annualized_mean_return=0.1260, daily_std=0.0101
TIP: annualized_mean_return=0.0000, daily_std=0.0008
Minimum required portfolio return (annualized): 0.0015
Market regime: sideways

Compute portfolio weights (w_EWJ, w_TIP) 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_TIP=X.XXXX

Answer: w_EWJ=0.0152, w_TIP=0.9848

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - -0.000001) / (0.000102 + 0.000001 - -0.000001)
  Unconstrained: w_EWJ=0.0107
  After long-only clamp: w_EWJ=0.0107, w_TIP=0.9893.


Question:
Assets: QUAL, ETH-USD
QUAL: annualized_mean_return=0.2016, daily_std=0.0066
ETH-USD: annualized_mean_return=2.4948, daily_std=0.0389
Minimum required portfolio return (annualized): 0.2584
Market regime: bull

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

Answer: w_QUAL=0.9602, w_ETH-USD=0.0398

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.001511 - -0.000020) / (0.000043 + 0.001511 - -0.000040)
  Unconstrained: w_QUAL=0.9603
  After long-only clamp: w_QUAL=0.9603, w_ETH-USD=0.0397.


Question:
Assets: BNB-USD, ITB
BNB-USD: annualized_mean_return=1.1592, daily_std=0.0229
ITB: annualized_mean_return=0.6300, daily_std=0.0189
Minimum required portfolio return (annualized): 1.0148
Market regime: bull

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

Answer: w_BNB-USD=0.7271, w_ITB=0.2729

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000357 - -0.000014) / (0.000523 + 0.000357 - -0.000027)
  Unconstrained: w_BNB-USD=0.4088
  After long-only clamp: w_BNB-USD=0.4088, w_ITB=0.5912.


Question:
Assets: QUAL, SGOV
QUAL: annualized_mean_return=-0.0756, daily_std=0.0129
SGOV: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0047
Market regime: sideways

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

Answer: w_QUAL=0.0001, w_SGOV=0.9999

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000168 + 0.000000 - -0.000001)
  Unconstrained: w_QUAL=0.0018
  After long-only clamp: w_QUAL=0.0018, w_SGOV=0.9982.


XRP-USD σ=0.0338, SGOV σ=0.0001, ρ=0.102. Min-variance weights: XRP-USD=0.000, SGOV=1.000.

Question:
Assets: XRP-USD, SGOV
XRP-USD: annualized_mean_return=-1.0080, daily_std=0.0338
SGOV: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0504
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_SGOV) 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_SGOV=X.XXXX

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

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.001146 + 0.000000 - 0.000001)
  Unconstrained: w_XRP-USD=-0.0004
  After long-only clamp: w_XRP-USD=0.0000, w_SGOV=1.0000.


Question:
Assets: EFA, SOL-USD
EFA: annualized_mean_return=0.5292, daily_std=0.0073
SOL-USD: annualized_mean_return=-0.2520, daily_std=0.0321
Minimum required portfolio return (annualized): 0.1250
Market regime: bull

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

Answer: w_EFA=0.9058, w_SOL-USD=0.0942

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.001033 - -0.000060) / (0.000054 + 0.001033 - -0.000120)
  Unconstrained: w_EFA=0.9059
  After long-only clamp: w_EFA=0.9059, w_SOL-USD=0.0941.


Question:
Assets: IVV, CSHI
IVV: annualized_mean_return=0.2268, daily_std=0.0078
CSHI: annualized_mean_return=0.0504, daily_std=0.0007
Minimum required portfolio return (annualized): 0.0517
Market regime: sideways

Compute portfolio weights (w_IVV, w_CSHI) 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_CSHI=X.XXXX

Answer: w_IVV=0.0079, w_CSHI=0.9921

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000060 + 0.000000 - -0.000000)
  Unconstrained: w_IVV=0.0103
  After long-only clamp: w_IVV=0.0103, w_CSHI=0.9897.


Question:
Assets: VTI, BIL
VTI: annualized_mean_return=0.1764, daily_std=0.0134
BIL: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.1208
Market regime: sideways

Compute portfolio weights (w_VTI, w_BIL) 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_BIL=X.XXXX

Answer: w_VTI=0.5587, w_BIL=0.4413

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000001) / (0.000179 + 0.000000 - -0.000001)
  Unconstrained: w_VTI=0.0031
  After long-only clamp: w_VTI=0.0031, w_BIL=0.9969.


Question:
Assets: XLF, IAU
XLF: annualized_mean_return=0.1008, daily_std=0.0085
IAU: annualized_mean_return=0.1008, daily_std=0.0098
Minimum required portfolio return (annualized): 0.1008
Market regime: bull

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

Answer: w_XLF=0.5685, w_IAU=0.4315

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000097 - -0.000008) / (0.000072 + 0.000097 - -0.000015)
  Unconstrained: w_XLF=0.5688
  After long-only clamp: w_XLF=0.5688, w_IAU=0.4312.


Question:
Assets: EEM, CORN
EEM: annualized_mean_return=0.2016, daily_std=0.0124
CORN: annualized_mean_return=-0.1512, daily_std=0.0086
Minimum required portfolio return (annualized): 0.1189
Market regime: sideways

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

Answer: w_EEM=0.7656, w_CORN=0.2344

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000074 - -0.000008) / (0.000153 + 0.000074 - -0.000016)
  Unconstrained: w_EEM=0.3377
  After long-only clamp: w_EEM=0.3377, w_CORN=0.6623.


Question:
Assets: XLK, ICSH
XLK: annualized_mean_return=-0.3528, daily_std=0.0206
ICSH: annualized_mean_return=0.0756, daily_std=0.0004
Minimum required portfolio return (annualized): 0.0472
Market regime: sideways

Compute portfolio weights (w_XLK, w_ICSH) 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_ICSH=X.XXXX

Answer: w_XLK=0.0000, w_ICSH=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.000423 + 0.000000 - 0.000001)
  Unconstrained: w_XLK=-0.0010
  After long-only clamp: w_XLK=0.0000, w_ICSH=1.0000.


ADA-USD σ=0.0589, ICSH σ=0.0004, ρ=0.078. Min-variance weights: ADA-USD=0.000, ICSH=1.000.

Question:
Assets: ADA-USD, ICSH
ADA-USD: annualized_mean_return=-0.2520, daily_std=0.0589
ICSH: annualized_mean_return=0.0756, daily_std=0.0004
Minimum required portfolio return (annualized): -0.0364
Market regime: bear

Compute portfolio weights (w_ADA-USD, w_ICSH) 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_ICSH=X.XXXX

Answer: w_ADA-USD=0.0000, w_ICSH=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000002) / (0.003475 + 0.000000 - 0.000003)
  Unconstrained: w_ADA-USD=-0.0004
  After long-only clamp: w_ADA-USD=0.0000, w_ICSH=1.0000.


Question:
Assets: BNB-USD, SOYB
BNB-USD: annualized_mean_return=1.3608, daily_std=0.0197
SOYB: annualized_mean_return=0.1260, daily_std=0.0092
Minimum required portfolio return (annualized): 0.8962
Market regime: bull

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

Answer: w_BNB-USD=0.6237, w_SOYB=0.3763

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000085 - -0.000000) / (0.000386 + 0.000085 - -0.000000)
  Unconstrained: w_BNB-USD=0.1799
  After long-only clamp: w_BNB-USD=0.1799, w_SOYB=0.8201.


AVAX-USD σ=0.0445, VCIT σ=0.0025, ρ=0.238. Min-variance weights: AVAX-USD=0.000, VCIT=1.000.

Question:
Assets: AVAX-USD, VCIT
AVAX-USD: annualized_mean_return=1.6128, daily_std=0.0445
VCIT: annualized_mean_return=0.1008, daily_std=0.0025
Minimum required portfolio return (annualized): 0.1008
Market regime: bull

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

Answer: w_AVAX-USD=0.0000, w_VCIT=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000006 - 0.000027) / (0.001984 + 0.000006 - 0.000053)
  Unconstrained: w_AVAX-USD=-0.0105
  After long-only clamp: w_AVAX-USD=0.0000, w_VCIT=1.0000.


Question:
Assets: ADA-USD, BIL
ADA-USD: annualized_mean_return=1.0080, daily_std=0.0383
BIL: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.5575
Market regime: bull

Compute portfolio weights (w_ADA-USD, w_BIL) 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_BIL=X.XXXX

Answer: w_ADA-USD=0.5296, w_BIL=0.4704

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.001470 + 0.000000 - 0.000000)
  Unconstrained: w_ADA-USD=-0.0001
  After long-only clamp: w_ADA-USD=0.0000, w_BIL=1.0000.


LINK-USD σ=0.0626, VNQ σ=0.0106, ρ=0.028. Min-variance weights: LINK-USD=0.024, VNQ=0.977.

Question:
Assets: LINK-USD, VNQ
LINK-USD: annualized_mean_return=1.5372, daily_std=0.0626
VNQ: annualized_mean_return=-0.3780, daily_std=0.0106
Minimum required portfolio return (annualized): 1.1460
Market regime: sideways

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

Answer: w_LINK-USD=0.7957, w_VNQ=0.2043

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000113 - 0.000019) / (0.003915 + 0.000113 - 0.000037)
  Unconstrained: w_LINK-USD=0.0235
  After long-only clamp: w_LINK-USD=0.0235, w_VNQ=0.9765.


Question:
Assets: EEM, SCHH
EEM: annualized_mean_return=0.4284, daily_std=0.0075
SCHH: annualized_mean_return=0.0756, daily_std=0.0087
Minimum required portfolio return (annualized): 0.3302
Market regime: bull

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

Answer: w_EEM=0.7217, w_SCHH=0.2783

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000075 - 0.000022) / (0.000056 + 0.000075 - 0.000043)
  Unconstrained: w_EEM=0.6077
  After long-only clamp: w_EEM=0.6077, w_SCHH=0.3923.


Question:
Assets: EFA, PDBC
EFA: annualized_mean_return=0.3024, daily_std=0.0107
PDBC: annualized_mean_return=-0.1260, daily_std=0.0109
Minimum required portfolio return (annualized): 0.0305
Market regime: sideways

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

Answer: w_EFA=0.5119, w_PDBC=0.4881

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000119 - 0.000019) / (0.000115 + 0.000119 - 0.000037)
  Unconstrained: w_EFA=0.5118
  After long-only clamp: w_EFA=0.5118, w_PDBC=0.4882.


Question:
Assets: DOT-USD, SOYB
DOT-USD: annualized_mean_return=0.3780, daily_std=0.0389
SOYB: annualized_mean_return=0.1512, daily_std=0.0090
Minimum required portfolio return (annualized): 0.1649
Market regime: bull

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

Answer: w_DOT-USD=0.0655, w_SOYB=0.9345

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000081 - -0.000027) / (0.001517 + 0.000081 - -0.000054)
  Unconstrained: w_DOT-USD=0.0655
  After long-only clamp: w_DOT-USD=0.0655, w_SOYB=0.9345.


Question:
Assets: QQQ, XHB
QQQ: annualized_mean_return=0.3780, daily_std=0.0074
XHB: annualized_mean_return=0.7560, daily_std=0.0177
Minimum required portfolio return (annualized): 0.3979
Market regime: bull

Compute portfolio weights (w_QQQ, w_XHB) 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_XHB=X.XXXX

Answer: w_QQQ=0.9235, w_XHB=0.0765

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000315 - 0.000032) / (0.000055 + 0.000315 - 0.000064)
  Unconstrained: w_QQQ=0.9240
  After long-only clamp: w_QQQ=0.9240, w_XHB=0.0760.


Question:
Assets: ^VIX, HAUZ
^VIX: annualized_mean_return=-1.4112, daily_std=0.0778
HAUZ: annualized_mean_return=-0.5040, daily_std=0.0091
Minimum required portfolio return (annualized): -0.5318
Market regime: sideways

Compute portfolio weights (w_^VIX, w_HAUZ) 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_HAUZ=X.XXXX

Answer: w_^VIX=0.0306, w_HAUZ=0.9694

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000083 - -0.000280) / (0.006046 + 0.000083 - -0.000560)
  Unconstrained: w_^VIX=0.0543
  After long-only clamp: w_^VIX=0.0543, w_HAUZ=0.9457.


Question:
Assets: USMV, VCIT
USMV: annualized_mean_return=-0.1260, daily_std=0.0066
VCIT: annualized_mean_return=0.0000, daily_std=0.0035
Minimum required portfolio return (annualized): -0.0075
Market regime: sideways

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

Answer: w_USMV=0.0595, w_VCIT=0.9405

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000012 - 0.000005) / (0.000043 + 0.000012 - 0.000010)
  Unconstrained: w_USMV=0.1623
  After long-only clamp: w_USMV=0.1623, w_VCIT=0.8377.


Question:
Assets: EFA, IYR
EFA: annualized_mean_return=0.1764, daily_std=0.0071
IYR: annualized_mean_return=-0.0756, daily_std=0.0079
Minimum required portfolio return (annualized): 0.0303
Market regime: sideways

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

Answer: w_EFA=0.6174, w_IYR=0.3826

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000062 - 0.000030) / (0.000050 + 0.000062 - 0.000059)
  Unconstrained: w_EFA=0.6157
  After long-only clamp: w_EFA=0.6157, w_IYR=0.3843.


MATIC-USD σ=0.0447, TLH σ=0.0063, ρ=0.005. Min-variance weights: MATIC-USD=0.019, TLH=0.981.

Question:
Assets: MATIC-USD, TLH
MATIC-USD: annualized_mean_return=-2.4444, daily_std=0.0447
TLH: annualized_mean_return=0.2268, daily_std=0.0063
Minimum required portfolio return (annualized): 0.1913
Market regime: bear

Compute portfolio weights (w_MATIC-USD, w_TLH) 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_TLH=X.XXXX

Answer: w_MATIC-USD=0.0133, w_TLH=0.9867

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000040 - 0.000002) / (0.001998 + 0.000040 - 0.000003)
  Unconstrained: w_MATIC-USD=0.0189
  After long-only clamp: w_MATIC-USD=0.0189, w_TLH=0.9811.


Question:
Assets: XLB, BIL
XLB: annualized_mean_return=0.0756, daily_std=0.0099
BIL: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0593
Market regime: bull

Compute portfolio weights (w_XLB, w_BIL) 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_BIL=X.XXXX

Answer: w_XLB=0.3532, w_BIL=0.6468

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000097 + 0.000000 - 0.000000)
  Unconstrained: w_XLB=-0.0010
  After long-only clamp: w_XLB=0.0000, w_BIL=1.0000.


MATIC-USD σ=0.0447, SGOV σ=0.0001, ρ=-0.101. Min-variance weights: MATIC-USD=0.000, SGOV=1.000.

Question:
Assets: MATIC-USD, SGOV
MATIC-USD: annualized_mean_return=-2.4444, daily_std=0.0447
SGOV: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0494
Market regime: bear

Compute portfolio weights (w_MATIC-USD, w_SGOV) 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_SGOV=X.XXXX

Answer: w_MATIC-USD=0.0004, w_SGOV=0.9996

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000001) / (0.001998 + 0.000000 - -0.000001)
  Unconstrained: w_MATIC-USD=0.0003
  After long-only clamp: w_MATIC-USD=0.0003, w_SGOV=0.9997.


Question:
Assets: XLY, XHB
XLY: annualized_mean_return=0.3024, daily_std=0.0115
XHB: annualized_mean_return=-0.3024, daily_std=0.0147
Minimum required portfolio return (annualized): -0.0504
Market regime: sideways

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

Answer: w_XLY=0.7521, w_XHB=0.2479

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000217 - 0.000089) / (0.000131 + 0.000217 - 0.000177)
  Unconstrained: w_XLY=0.7510
  After long-only clamp: w_XLY=0.7510, w_XHB=0.2490.


Question:
Assets: FXI, LQD
FXI: annualized_mean_return=0.2520, daily_std=0.0134
LQD: annualized_mean_return=0.0756, daily_std=0.0031
Minimum required portfolio return (annualized): 0.1180
Market regime: bull

Compute portfolio weights (w_FXI, w_LQD) 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_LQD=X.XXXX

Answer: w_FXI=0.2404, w_LQD=0.7596

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000010 - 0.000004) / (0.000180 + 0.000010 - 0.000009)
  Unconstrained: w_FXI=0.0302
  After long-only clamp: w_FXI=0.0302, w_LQD=0.9698.


Question:
Assets: IWM, ITB
IWM: annualized_mean_return=-0.5796, daily_std=0.0113
ITB: annualized_mean_return=-0.7056, daily_std=0.0158
Minimum required portfolio return (annualized): -0.6365
Market regime: sideways

Compute portfolio weights (w_IWM, w_ITB) 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_ITB=X.XXXX

Answer: w_IWM=0.8801, w_ITB=0.1199

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000250 - 0.000108) / (0.000127 + 0.000250 - 0.000217)
  Unconstrained: w_IWM=0.8824
  After long-only clamp: w_IWM=0.8824, w_ITB=0.1176.


ETH-USD σ=0.0376, MORT σ=0.0170, ρ=0.103. Min-variance weights: ETH-USD=0.142, MORT=0.858.

Question:
Assets: ETH-USD, MORT
ETH-USD: annualized_mean_return=1.8396, daily_std=0.0376
MORT: annualized_mean_return=-0.1764, daily_std=0.0170
Minimum required portfolio return (annualized): 0.6149
Market regime: sideways

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

Answer: w_ETH-USD=0.3925, w_MORT=0.6075

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000290 - 0.000066) / (0.001416 + 0.000290 - 0.000132)
  Unconstrained: w_ETH-USD=0.1423
  After long-only clamp: w_ETH-USD=0.1423, w_MORT=0.8577.


Question:
Assets: VEA, BNDX
VEA: annualized_mean_return=0.2520, daily_std=0.0103
BNDX: annualized_mean_return=0.1260, daily_std=0.0024
Minimum required portfolio return (annualized): 0.1561
Market regime: sideways

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

Answer: w_VEA=0.2389, w_BNDX=0.7611

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000006 - 0.000002) / (0.000106 + 0.000006 - 0.000003)
  Unconstrained: w_VEA=0.0366
  After long-only clamp: w_VEA=0.0366, w_BNDX=0.9634.


Question:
Assets: XLV, PPLT
XLV: annualized_mean_return=0.3528, daily_std=0.0078
PPLT: annualized_mean_return=0.7056, daily_std=0.0191
Minimum required portfolio return (annualized): 0.3787
Market regime: sideways

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

Answer: w_XLV=0.8398, w_PPLT=0.1602

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000366 - -0.000011) / (0.000061 + 0.000366 - -0.000022)
  Unconstrained: w_XLV=0.8399
  After long-only clamp: w_XLV=0.8399, w_PPLT=0.1601.


Question:
Assets: XLY, SHV
XLY: annualized_mean_return=-0.3528, daily_std=0.0187
SHV: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0504
Market regime: sideways

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

Answer: w_XLY=-0.0000, w_SHV=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000352 + 0.000000 - 0.000000)
  Unconstrained: w_XLY=0.0000
  After long-only clamp: w_XLY=0.0000, w_SHV=1.0000.


BNB-USD σ=0.0229, HAUZ σ=0.0102, ρ=0.031. Min-variance weights: BNB-USD=0.157, HAUZ=0.844.

Question:
Assets: BNB-USD, HAUZ
BNB-USD: annualized_mean_return=-0.0252, daily_std=0.0229
HAUZ: annualized_mean_return=0.3276, daily_std=0.0102
Minimum required portfolio return (annualized): 0.2861
Market regime: sideways

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

Answer: w_BNB-USD=0.1176, w_HAUZ=0.8824

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000103 - 0.000007) / (0.000525 + 0.000103 - 0.000015)
  Unconstrained: w_BNB-USD=0.1565
  After long-only clamp: w_BNB-USD=0.1565, w_HAUZ=0.8435.


Question:
Assets: XLK, TLH
XLK: annualized_mean_return=-0.0756, daily_std=0.0123
TLH: annualized_mean_return=-0.2016, daily_std=0.0068
Minimum required portfolio return (annualized): -0.1748
Market regime: sideways

Compute portfolio weights (w_XLK, w_TLH) 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_TLH=X.XXXX

Answer: w_XLK=0.2601, w_TLH=0.7399

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000046 - -0.000012) / (0.000152 + 0.000046 - -0.000023)
  Unconstrained: w_XLK=0.2593
  After long-only clamp: w_XLK=0.2593, w_TLH=0.7407.


Question:
Assets: XRP-USD, BIL
XRP-USD: annualized_mean_return=-0.2772, daily_std=0.0677
BIL: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): -0.0475
Market regime: bear

Compute portfolio weights (w_XRP-USD, w_BIL) 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_BIL=X.XXXX

Answer: w_XRP-USD=0.0002, w_BIL=0.9998

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000001) / (0.004577 + 0.000000 - -0.000003)
  Unconstrained: w_XRP-USD=0.0003
  After long-only clamp: w_XRP-USD=0.0003, w_BIL=0.9997.


Question:
Assets: QUAL, USO
QUAL: annualized_mean_return=0.2268, daily_std=0.0068
USO: annualized_mean_return=-0.6552, daily_std=0.0148
Minimum required portfolio return (annualized): -0.2264
Market regime: bull

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

Answer: w_QUAL=0.8773, w_USO=0.1227

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000220 - 0.000018) / (0.000046 + 0.000220 - 0.000035)
  Unconstrained: w_QUAL=0.8764
  After long-only clamp: w_QUAL=0.8764, w_USO=0.1236.


Question:
Assets: ETH-USD, STIP
ETH-USD: annualized_mean_return=2.5704, daily_std=0.0331
STIP: annualized_mean_return=0.0756, daily_std=0.0010
Minimum required portfolio return (annualized): 0.0931
Market regime: bull

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

Answer: w_ETH-USD=0.0090, w_STIP=0.9910

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - -0.000009) / (0.001092 + 0.000001 - -0.000018)
  Unconstrained: w_ETH-USD=0.0090
  After long-only clamp: w_ETH-USD=0.0090, w_STIP=0.9910.


Question:
Assets: XLB, SGOV
XLB: annualized_mean_return=-0.2520, daily_std=0.0087
SGOV: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0503
Market regime: sideways

Compute portfolio weights (w_XLB, w_SGOV) 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_SGOV=X.XXXX

Answer: w_XLB=0.0003, w_SGOV=0.9997

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000076 + 0.000000 - -0.000000)
  Unconstrained: w_XLB=0.0006
  After long-only clamp: w_XLB=0.0006, w_SGOV=0.9994.


Question:
Assets: VLUE, DBC
VLUE: annualized_mean_return=-0.4788, daily_std=0.0131
DBC: annualized_mean_return=-0.1260, daily_std=0.0099
Minimum required portfolio return (annualized): -0.3471
Market regime: bear

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

Answer: w_VLUE=0.1414, w_DBC=0.8586

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000098 - 0.000084) / (0.000171 + 0.000098 - 0.000168)
  Unconstrained: w_VLUE=0.1419
  After long-only clamp: w_VLUE=0.1419, w_DBC=0.8581.


Question:
Assets: XLF, CPER
XLF: annualized_mean_return=-0.1764, daily_std=0.0129
CPER: annualized_mean_return=-0.2520, daily_std=0.0168
Minimum required portfolio return (annualized): -0.2189
Market regime: bear

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

Answer: w_XLF=0.6783, w_CPER=0.3217

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000282 - 0.000063) / (0.000167 + 0.000282 - 0.000126)
  Unconstrained: w_XLF=0.6783
  After long-only clamp: w_XLF=0.6783, w_CPER=0.3217.


Question:
Assets: QUAL, TLT
QUAL: annualized_mean_return=0.1512, daily_std=0.0077
TLT: annualized_mean_return=-0.0756, daily_std=0.0078
Minimum required portfolio return (annualized): 0.0165
Market regime: sideways

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

Answer: w_QUAL=0.5069, w_TLT=0.4931

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000060 - -0.000006) / (0.000059 + 0.000060 - -0.000012)
  Unconstrained: w_QUAL=0.5069
  After long-only clamp: w_QUAL=0.5069, w_TLT=0.4931.


Question:
Assets: ETH-USD, LQD
ETH-USD: annualized_mean_return=1.8396, daily_std=0.0313
LQD: annualized_mean_return=0.1260, daily_std=0.0039
Minimum required portfolio return (annualized): 0.8779
Market regime: bull

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

Answer: w_ETH-USD=0.4388, w_LQD=0.5612

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000015 - -0.000016) / (0.000982 + 0.000015 - -0.000032)
  Unconstrained: w_ETH-USD=0.0299
  After long-only clamp: w_ETH-USD=0.0299, w_LQD=0.9701.


Question:
Assets: IVV, DBB
IVV: annualized_mean_return=0.2268, daily_std=0.0085
DBB: annualized_mean_return=-0.1008, daily_std=0.0093
Minimum required portfolio return (annualized): 0.0199
Market regime: sideways

Compute portfolio weights (w_IVV, w_DBB) 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_DBB=X.XXXX

Answer: w_IVV=0.5414, w_DBB=0.4586

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000087 - -0.000009) / (0.000072 + 0.000087 - -0.000019)
  Unconstrained: w_IVV=0.5413
  After long-only clamp: w_IVV=0.5413, w_DBB=0.4587.


Question:
Assets: SOL-USD, XLI
SOL-USD: annualized_mean_return=0.1260, daily_std=0.0360
XLI: annualized_mean_return=0.6048, daily_std=0.0117
Minimum required portfolio return (annualized): 0.5916
Market regime: sideways

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

Answer: w_SOL-USD=0.0276, w_XLI=0.9724

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000137 - 0.000016) / (0.001295 + 0.000137 - 0.000032)
  Unconstrained: w_SOL-USD=0.0862
  After long-only clamp: w_SOL-USD=0.0862, w_XLI=0.9138.


Question:
Assets: EEM, BIL
EEM: annualized_mean_return=-0.0756, daily_std=0.0086
BIL: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): -0.0180
Market regime: sideways

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

Answer: w_EEM=0.0003, w_BIL=0.9997

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000074 + 0.000000 - 0.000000)
  Unconstrained: w_EEM=-0.0018
  After long-only clamp: w_EEM=0.0000, w_BIL=1.0000.


Question:
Assets: DOT-USD, REZ
DOT-USD: annualized_mean_return=-1.6884, daily_std=0.0492
REZ: annualized_mean_return=-0.0000, daily_std=0.0085
Minimum required portfolio return (annualized): -0.0173
Market regime: sideways

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

Answer: w_DOT-USD=0.0102, w_REZ=0.9898

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000073 - 0.000026) / (0.002425 + 0.000073 - 0.000053)
  Unconstrained: w_DOT-USD=0.0190
  After long-only clamp: w_DOT-USD=0.0190, w_REZ=0.9810.


Question:
Assets: ACWI, VNQ
ACWI: annualized_mean_return=0.3276, daily_std=0.0061
VNQ: annualized_mean_return=0.0756, daily_std=0.0091
Minimum required portfolio return (annualized): 0.1957
Market regime: bull

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

Answer: w_ACWI=0.8703, w_VNQ=0.1297

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000082 - 0.000030) / (0.000038 + 0.000082 - 0.000061)
  Unconstrained: w_ACWI=0.8742
  After long-only clamp: w_ACWI=0.8742, w_VNQ=0.1258.


VLUE σ=0.0126, SOL-USD σ=0.0633, ρ=0.253. Min-variance weights: VLUE=1.000, SOL-USD=0.000.

Question:
Assets: VLUE, SOL-USD
VLUE: annualized_mean_return=-0.3780, daily_std=0.0126
SOL-USD: annualized_mean_return=-1.8900, daily_std=0.0633
Minimum required portfolio return (annualized): -0.9949
Market regime: bear

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

Answer: w_VLUE=1.0000, w_SOL-USD=0.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.004004 - 0.000201) / (0.000158 + 0.004004 - 0.000402)
  Unconstrained: w_VLUE=1.0115
  After long-only clamp: w_VLUE=1.0000, w_SOL-USD=0.0000.


Question:
Assets: BTC-USD, VNQ
BTC-USD: annualized_mean_return=0.2016, daily_std=0.0178
VNQ: annualized_mean_return=0.1008, daily_std=0.0079
Minimum required portfolio return (annualized): 0.1830
Market regime: bull

Compute portfolio weights (w_BTC-USD, w_VNQ) 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_VNQ=X.XXXX

Answer: w_BTC-USD=0.8155, w_VNQ=0.1845

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000063 - -0.000009) / (0.000316 + 0.000063 - -0.000019)
  Unconstrained: w_BTC-USD=0.1814
  After long-only clamp: w_BTC-USD=0.1814, w_VNQ=0.8186.


Question:
Assets: VTI, ICSH
VTI: annualized_mean_return=-0.4032, daily_std=0.0141
ICSH: annualized_mean_return=0.0756, daily_std=0.0004
Minimum required portfolio return (annualized): 0.0384
Market regime: bear

Compute portfolio weights (w_VTI, w_ICSH) 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_ICSH=X.XXXX

Answer: w_VTI=0.0000, w_ICSH=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.000200 + 0.000000 - 0.000002)
  Unconstrained: w_VTI=-0.0034
  After long-only clamp: w_VTI=0.0000, w_ICSH=1.0000.


BNB-USD σ=0.0294, ICSH σ=0.0003, ρ=0.064. Min-variance weights: BNB-USD=0.000, ICSH=1.000.

Question:
Assets: BNB-USD, ICSH
BNB-USD: annualized_mean_return=0.2520, daily_std=0.0294
ICSH: annualized_mean_return=0.0504, daily_std=0.0003
Minimum required portfolio return (annualized): 0.1008
Market regime: sideways

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

Answer: w_BNB-USD=0.2500, w_ICSH=0.7500

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.000864 + 0.000000 - 0.000001)
  Unconstrained: w_BNB-USD=-0.0005
  After long-only clamp: w_BNB-USD=0.0000, w_ICSH=1.0000.


Question:
Assets: BNB-USD, CPER
BNB-USD: annualized_mean_return=0.1512, daily_std=0.0231
CPER: annualized_mean_return=-0.2016, daily_std=0.0189
Minimum required portfolio return (annualized): -0.1265
Market regime: sideways

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

Answer: w_BNB-USD=0.4165, w_CPER=0.5835

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000355 - -0.000085) / (0.000532 + 0.000355 - -0.000171)
  Unconstrained: w_BNB-USD=0.4165
  After long-only clamp: w_BNB-USD=0.4165, w_CPER=0.5835.


AVAX-USD σ=0.0582, LQD σ=0.0052, ρ=0.057. Min-variance weights: AVAX-USD=0.003, LQD=0.997.

Question:
Assets: AVAX-USD, LQD
AVAX-USD: annualized_mean_return=0.4284, daily_std=0.0582
LQD: annualized_mean_return=0.1008, daily_std=0.0052
Minimum required portfolio return (annualized): 0.1017
Market regime: bear

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

Answer: w_AVAX-USD=0.0031, w_LQD=0.9969

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000027 - 0.000017) / (0.003389 + 0.000027 - 0.000035)
  Unconstrained: w_AVAX-USD=0.0030
  After long-only clamp: w_AVAX-USD=0.0030, w_LQD=0.9970.


XLI σ=0.0069, LINK-USD σ=0.0510, ρ=0.044. Min-variance weights: XLI=0.988, LINK-USD=0.012.

Question:
Assets: XLI, LINK-USD
XLI: annualized_mean_return=0.3024, daily_std=0.0069
LINK-USD: annualized_mean_return=2.7468, daily_std=0.0510
Minimum required portfolio return (annualized): 0.3156
Market regime: bull

Compute portfolio weights (w_XLI, w_LINK-USD) 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_LINK-USD=X.XXXX

Answer: w_XLI=0.9879, w_LINK-USD=0.0121

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.002598 - 0.000016) / (0.000048 + 0.002598 - 0.000031)
  Unconstrained: w_XLI=0.9878
  After long-only clamp: w_XLI=0.9878, w_LINK-USD=0.0122.


BTC-USD σ=0.0228, CSHI σ=0.0007, ρ=0.155. Min-variance weights: BTC-USD=0.000, CSHI=1.000.

Question:
Assets: BTC-USD, CSHI
BTC-USD: annualized_mean_return=-0.7812, daily_std=0.0228
CSHI: annualized_mean_return=0.0504, daily_std=0.0007
Minimum required portfolio return (annualized): -0.1564
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_CSHI) 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_CSHI=X.XXXX

Answer: w_BTC-USD=0.0000, w_CSHI=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000002) / (0.000518 + 0.000000 - 0.000005)
  Unconstrained: w_BTC-USD=-0.0038
  After long-only clamp: w_BTC-USD=0.0000, w_CSHI=1.0000.


Question:
Assets: QUAL, DBC
QUAL: annualized_mean_return=0.2772, daily_std=0.0058
DBC: annualized_mean_return=0.0504, daily_std=0.0069
Minimum required portfolio return (annualized): 0.1491
Market regime: bull

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

Answer: w_QUAL=0.5831, w_DBC=0.4169

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000048 - -0.000004) / (0.000033 + 0.000048 - -0.000008)
  Unconstrained: w_QUAL=0.5833
  After long-only clamp: w_QUAL=0.5833, w_DBC=0.4167.


Question:
Assets: USMV, USO
USMV: annualized_mean_return=0.0000, daily_std=0.0097
USO: annualized_mean_return=-0.4032, daily_std=0.0222
Minimum required portfolio return (annualized): -0.0034
Market regime: sideways

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

Answer: w_USMV=0.9916, w_USO=0.0084

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000493 - 0.000083) / (0.000093 + 0.000493 - 0.000165)
  Unconstrained: w_USMV=0.9745
  After long-only clamp: w_USMV=0.9745, w_USO=0.0255.


Question:
Assets: IWM, VNQI
IWM: annualized_mean_return=0.4284, daily_std=0.0113
VNQI: annualized_mean_return=0.2016, daily_std=0.0063
Minimum required portfolio return (annualized): 0.2189
Market regime: bull

Compute portfolio weights (w_IWM, w_VNQI) 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_VNQI=X.XXXX

Answer: w_IWM=0.0856, w_VNQI=0.9144

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000039 - 0.000030) / (0.000128 + 0.000039 - 0.000060)
  Unconstrained: w_IWM=0.0855
  After long-only clamp: w_IWM=0.0855, w_VNQI=0.9145.


Question:
Assets: XLF, REZ
XLF: annualized_mean_return=-0.0252, daily_std=0.0150
REZ: annualized_mean_return=-0.1008, daily_std=0.0132
Minimum required portfolio return (annualized): -0.0646
Market regime: sideways

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

Answer: w_XLF=0.4788, w_REZ=0.5212

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000175 - 0.000130) / (0.000224 + 0.000175 - 0.000259)
  Unconstrained: w_XLF=0.3245
  After long-only clamp: w_XLF=0.3245, w_REZ=0.6755.


Question:
Assets: IWM, SGOV
IWM: annualized_mean_return=0.3780, daily_std=0.0117
SGOV: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0504
Market regime: bull

Compute portfolio weights (w_IWM, w_SGOV) 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_SGOV=X.XXXX

Answer: w_IWM=0.0002, w_SGOV=0.9998

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000137 + 0.000000 - -0.000000)
  Unconstrained: w_IWM=0.0008
  After long-only clamp: w_IWM=0.0008, w_SGOV=0.9992.


Question:
Assets: XLRE, WEAT
XLRE: annualized_mean_return=0.0252, daily_std=0.0087
WEAT: annualized_mean_return=-0.1008, daily_std=0.0137
Minimum required portfolio return (annualized): 0.0115
Market regime: bull

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

Answer: w_XLRE=0.8913, w_WEAT=0.1087

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000187 - 0.000005) / (0.000076 + 0.000187 - 0.000010)
  Unconstrained: w_XLRE=0.7185
  After long-only clamp: w_XLRE=0.7185, w_WEAT=0.2815.


Question:
Assets: VTI, BIL
VTI: annualized_mean_return=-0.6804, daily_std=0.0130
BIL: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0503
Market regime: bear

Compute portfolio weights (w_VTI, w_BIL) 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_BIL=X.XXXX

Answer: w_VTI=0.0001, w_BIL=0.9999

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000169 + 0.000000 - 0.000000)
  Unconstrained: w_VTI=-0.0005
  After long-only clamp: w_VTI=0.0000, w_BIL=1.0000.


LINK-USD σ=0.0517, ICSH σ=0.0003, ρ=-0.113. Min-variance weights: LINK-USD=0.001, ICSH=0.999.

Question:
Assets: LINK-USD, ICSH
LINK-USD: annualized_mean_return=2.7972, daily_std=0.0517
ICSH: annualized_mean_return=0.0756, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0775
Market regime: bull

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

Answer: w_LINK-USD=0.0008, w_ICSH=0.9992

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000002) / (0.002677 + 0.000000 - -0.000004)
  Unconstrained: w_LINK-USD=0.0008
  After long-only clamp: w_LINK-USD=0.0008, w_ICSH=0.9992.


BTC-USD σ=0.0179, BNDX σ=0.0022, ρ=0.056. Min-variance weights: BTC-USD=0.008, BNDX=0.992.

Question:
Assets: BTC-USD, BNDX
BTC-USD: annualized_mean_return=0.5796, daily_std=0.0179
BNDX: annualized_mean_return=0.1008, daily_std=0.0022
Minimum required portfolio return (annualized): 0.3827
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_BNDX) 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_BNDX=X.XXXX

Answer: w_BTC-USD=0.5888, w_BNDX=0.4112

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000005 - 0.000002) / (0.000321 + 0.000005 - 0.000004)
  Unconstrained: w_BTC-USD=0.0079
  After long-only clamp: w_BTC-USD=0.0079, w_BNDX=0.9921.


Question:
Assets: XLY, STIP
XLY: annualized_mean_return=0.3024, daily_std=0.0095
STIP: annualized_mean_return=0.0504, daily_std=0.0010
Minimum required portfolio return (annualized): 0.2021
Market regime: bull

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

Answer: w_XLY=0.6020, w_STIP=0.3980

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - -0.000000) / (0.000090 + 0.000001 - -0.000000)
  Unconstrained: w_XLY=0.0128
  After long-only clamp: w_XLY=0.0128, w_STIP=0.9872.


MATIC-USD σ=0.0493, PDBC σ=0.0074, ρ=-0.072. Min-variance weights: MATIC-USD=0.032, PDBC=0.968.

Question:
Assets: MATIC-USD, PDBC
MATIC-USD: annualized_mean_return=-3.1248, daily_std=0.0493
PDBC: annualized_mean_return=0.2268, daily_std=0.0074
Minimum required portfolio return (annualized): 0.1966
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_PDBC) 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_PDBC=X.XXXX

Answer: w_MATIC-USD=0.0090, w_PDBC=0.9910

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000054 - -0.000026) / (0.002432 + 0.000054 - -0.000052)
  Unconstrained: w_MATIC-USD=0.0316
  After long-only clamp: w_MATIC-USD=0.0316, w_PDBC=0.9684.


Question:
Assets: BTC-USD, STIP
BTC-USD: annualized_mean_return=1.5372, daily_std=0.0286
STIP: annualized_mean_return=0.0252, daily_std=0.0010
Minimum required portfolio return (annualized): 0.0439
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_STIP) 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_STIP=X.XXXX

Answer: w_BTC-USD=0.0130, w_STIP=0.9870

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - -0.000010) / (0.000819 + 0.000001 - -0.000019)
  Unconstrained: w_BTC-USD=0.0126
  After long-only clamp: w_BTC-USD=0.0126, w_STIP=0.9874.


Question:
Assets: IWM, SGOV
IWM: annualized_mean_return=0.6048, daily_std=0.0113
SGOV: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0505
Market regime: bull

Compute portfolio weights (w_IWM, w_SGOV) 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_SGOV=X.XXXX

Answer: w_IWM=0.0002, w_SGOV=0.9998

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000127 + 0.000000 - -0.000000)
  Unconstrained: w_IWM=0.0010
  After long-only clamp: w_IWM=0.0010, w_SGOV=0.9990.


Question:
Assets: EEM, SCHH
EEM: annualized_mean_return=0.0252, daily_std=0.0087
SCHH: annualized_mean_return=-0.1008, daily_std=0.0104
Minimum required portfolio return (annualized): 0.0037
Market regime: sideways

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

Answer: w_EEM=0.8294, w_SCHH=0.1706

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000109 - 0.000035) / (0.000075 + 0.000109 - 0.000070)
  Unconstrained: w_EEM=0.6459
  After long-only clamp: w_EEM=0.6459, w_SCHH=0.3541.


Question:
Assets: LINK-USD, TLH
LINK-USD: annualized_mean_return=-1.8144, daily_std=0.0568
TLH: annualized_mean_return=0.2268, daily_std=0.0061
Minimum required portfolio return (annualized): -0.4249
Market regime: sideways

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

Answer: w_LINK-USD=0.0259, w_TLH=0.9741

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000037 - -0.000050) / (0.003230 + 0.000037 - -0.000101)
  Unconstrained: w_LINK-USD=0.0260
  After long-only clamp: w_LINK-USD=0.0260, w_TLH=0.9740.


LINK-USD σ=0.0635, CPER σ=0.0123, ρ=-0.085. Min-variance weights: LINK-USD=0.050, CPER=0.950.

Question:
Assets: LINK-USD, CPER
LINK-USD: annualized_mean_return=1.2096, daily_std=0.0635
CPER: annualized_mean_return=-0.0252, daily_std=0.0123
Minimum required portfolio return (annualized): 0.0251
Market regime: sideways

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

Answer: w_LINK-USD=0.0501, w_CPER=0.9499

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000150 - -0.000066) / (0.004035 + 0.000150 - -0.000132)
  Unconstrained: w_LINK-USD=0.0502
  After long-only clamp: w_LINK-USD=0.0502, w_CPER=0.9498.


Question:
Assets: BNB-USD, XLP
BNB-USD: annualized_mean_return=0.8820, daily_std=0.0166
XLP: annualized_mean_return=0.0504, daily_std=0.0069
Minimum required portfolio return (annualized): 0.3195
Market regime: bull

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

Answer: w_BNB-USD=0.3236, w_XLP=0.6764

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000048 - 0.000015) / (0.000277 + 0.000048 - 0.000030)
  Unconstrained: w_BNB-USD=0.1110
  After long-only clamp: w_BNB-USD=0.1110, w_XLP=0.8890.


Question:
Assets: XLB, DOT-USD
XLB: annualized_mean_return=0.1260, daily_std=0.0139
DOT-USD: annualized_mean_return=0.9576, daily_std=0.0378
Minimum required portfolio return (annualized): 0.1569
Market regime: sideways

Compute portfolio weights (w_XLB, w_DOT-USD) 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_DOT-USD=X.XXXX

Answer: w_XLB=0.9117, w_DOT-USD=0.0883

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.001426 - 0.000062) / (0.000194 + 0.001426 - 0.000123)
  Unconstrained: w_XLB=0.9115
  After long-only clamp: w_XLB=0.9115, w_DOT-USD=0.0885.


ETH-USD σ=0.0388, SGOV σ=0.0002, ρ=0.051. Min-variance weights: ETH-USD=0.000, SGOV=1.000.

Question:
Assets: ETH-USD, SGOV
ETH-USD: annualized_mean_return=0.7308, daily_std=0.0388
SGOV: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0504
Market regime: bull

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

Answer: w_ETH-USD=0.0000, w_SGOV=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.001503 + 0.000000 - 0.000001)
  Unconstrained: w_ETH-USD=-0.0002
  After long-only clamp: w_ETH-USD=0.0000, w_SGOV=1.0000.


Question:
Assets: XLI, VNQI
XLI: annualized_mean_return=-0.1008, daily_std=0.0136
VNQI: annualized_mean_return=0.3276, daily_std=0.0093
Minimum required portfolio return (annualized): 0.3195
Market regime: sideways

Compute portfolio weights (w_XLI, w_VNQI) 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_VNQI=X.XXXX

Answer: w_XLI=0.0189, w_VNQI=0.9811

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000086 - 0.000075) / (0.000184 + 0.000086 - 0.000151)
  Unconstrained: w_XLI=0.0900
  After long-only clamp: w_XLI=0.0900, w_VNQI=0.9100.


DOT-USD σ=0.0454, CSHI σ=0.0006, ρ=0.174. Min-variance weights: DOT-USD=0.000, CSHI=1.000.

Question:
Assets: DOT-USD, CSHI
DOT-USD: annualized_mean_return=-1.0836, daily_std=0.0454
CSHI: annualized_mean_return=0.0504, daily_std=0.0006
Minimum required portfolio return (annualized): -0.2324
Market regime: sideways

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

Answer: w_DOT-USD=0.0000, w_CSHI=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000005) / (0.002061 + 0.000000 - 0.000010)
  Unconstrained: w_DOT-USD=-0.0022
  After long-only clamp: w_DOT-USD=0.0000, w_CSHI=1.0000.


LINK-USD σ=0.0472, BNO σ=0.0146, ρ=0.052. Min-variance weights: LINK-USD=0.074, BNO=0.925.

Question:
Assets: LINK-USD, BNO
LINK-USD: annualized_mean_return=-0.8064, daily_std=0.0472
BNO: annualized_mean_return=-0.4536, daily_std=0.0146
Minimum required portfolio return (annualized): -0.5313
Market regime: bull

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

Answer: w_LINK-USD=0.0744, w_BNO=0.9256

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000212 - 0.000036) / (0.002225 + 0.000212 - 0.000072)
  Unconstrained: w_LINK-USD=0.0745
  After long-only clamp: w_LINK-USD=0.0745, w_BNO=0.9255.


4-asset optimization. Max-Sharpe: 0.185. Portfolio: return=7.38%, vol=18.26%. Weights: w_QQQ=1.0000, w_XRP-USD=0.0000, w_IGOV=0.0000, w_REZ=0.0000.

Question:
Assets: QQQ, XRP-USD, IGOV, REZ
Annualized mean returns: QQQ:0.0738, XRP-USD:-2.1648, IGOV:-0.0114, REZ:-0.0626
Covariance matrix (annualized):
[[0.033336, 0.056593, 0.001731, -0.002864], [0.056593, 0.387307, 0.002656, -0.000389], [0.001731, 0.002656, 0.002677, 0.001857], [-0.002864, -0.000389, 0.001857, 0.020961]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QQQ=1.0000, w_XRP-USD=0.0000, w_IGOV=0.0000, w_REZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=1.0000, w_XRP-USD=0.0000, w_IGOV=0.0000, w_REZ=0.0000
Portfolio annualized return: 7.38%, volatility: 18.26%
Sharpe ratio: (0.0738 - 0.0400) / 0.1826 = 0.1849


4-asset optimization. Max-Sharpe: 7.307. Portfolio: return=128.96%, vol=17.10%. Weights: w_XLE=0.0408, w_BTC-USD=0.0000, w_REZ=0.0139, w_GLD=0.9453.

Question:
Assets: XLE, BTC-USD, REZ, GLD
Annualized mean returns: XLE:-0.0275, BTC-USD:-0.4041, REZ:0.0860, GLD:1.3642
Covariance matrix (annualized):
[[0.032443, 0.015183, 0.00166, -0.003098], [0.015183, 0.104165, -0.005615, 0.003206], [0.00166, -0.005615, 0.014375, 0.000856], [-0.003098, 0.003206, 0.000856, 0.032911]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_XLE=0.0408, w_BTC-USD=0.0000, w_REZ=0.0139, w_GLD=0.9453

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.0408, w_BTC-USD=0.0000, w_REZ=0.0139, w_GLD=0.9453
Portfolio annualized return: 128.96%, volatility: 17.10%
Sharpe ratio: (1.2896 - 0.0400) / 0.1710 = 7.3065


4-asset optimization. Max-Sharpe: 1.291. Portfolio: return=5.49%, vol=1.15%. Weights: w_XLF=0.0000, w_BTC-USD=0.0000, w_VNQ=0.0000, w_CSHI=1.0000.

Question:
Assets: XLF, BTC-USD, VNQ, CSHI
Annualized mean returns: XLF:0.0184, BTC-USD:-2.4667, VNQ:0.0043, CSHI:0.0549
Covariance matrix (annualized):
[[0.024178, 0.031554, 0.014326, 0.00054], [0.031554, 0.171106, 0.015982, 0.001341], [0.014326, 0.015982, 0.019973, 0.000463], [0.00054, 0.001341, 0.000463, 0.000133]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_XLF=0.0000, w_BTC-USD=0.0000, w_VNQ=0.0000, w_CSHI=1.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLF=0.0000, w_BTC-USD=0.0000, w_VNQ=0.0000, w_CSHI=1.0000
Portfolio annualized return: 5.49%, volatility: 1.15%
Sharpe ratio: (0.0549 - 0.0400) / 0.0115 = 1.2906


4-asset optimization. Max-Sharpe: 4.315. Portfolio: return=5.37%, vol=0.32%. Weights: w_QUAL=0.0000, w_SOL-USD=0.0000, w_ICSH=0.9974, w_DBB=0.0026.

Question:
Assets: QUAL, SOL-USD, ICSH, DBB
Annualized mean returns: QUAL:0.1384, SOL-USD:-0.7355, ICSH:0.0533, DBB:0.2040
Covariance matrix (annualized):
[[0.014461, 0.0159, 0.000142, 0.00558], [0.0159, 0.299291, 0.000413, 0.020013], [0.000142, 0.000413, 1e-05, 8.1e-05], [0.00558, 0.020013, 8.1e-05, 0.015187]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_QUAL=0.0000, w_SOL-USD=0.0000, w_ICSH=0.9974, w_DBB=0.0026

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0000, w_SOL-USD=0.0000, w_ICSH=0.9974, w_DBB=0.0026
Portfolio annualized return: 5.37%, volatility: 0.32%
Sharpe ratio: (0.0537 - 0.0400) / 0.0032 = 4.3151


4-asset optimization. Max-Sharpe: 1.800. Portfolio: return=6.73%, vol=1.51%. Weights: w_XLV=0.0000, w_BTC-USD=0.0134, w_SHY=0.9842, w_PPLT=0.0024.

Question:
Assets: XLV, BTC-USD, SHY, PPLT
Annualized mean returns: XLV:-0.3790, BTC-USD:0.2376, SHY:0.0651, PPLT:-0.0016
Covariance matrix (annualized):
[[0.034805, 0.023514, -8.9e-05, 0.008974], [0.023514, 0.293137, -0.002342, 0.013667], [-8.9e-05, -0.002342, 0.000248, -0.000618], [0.008974, 0.013667, -0.000618, 0.031301]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bear

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

Answer: w_XLV=0.0000, w_BTC-USD=0.0134, w_SHY=0.9842, w_PPLT=0.0024

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0000, w_BTC-USD=0.0134, w_SHY=0.9842, w_PPLT=0.0024
Portfolio annualized return: 6.73%, volatility: 1.51%
Sharpe ratio: (0.0673 - 0.0400) / 0.0151 = 1.7999


4-asset optimization. Max-Sharpe: 3.854. Portfolio: return=49.12%, vol=11.71%. Weights: w_XLV=0.0000, w_ETH-USD=0.1098, w_HAUZ=0.8902, w_TLT=0.0000.

Question:
Assets: XLV, ETH-USD, HAUZ, TLT
Annualized mean returns: XLV:0.2025, ETH-USD:1.4916, HAUZ:0.3678, TLT:0.0491
Covariance matrix (annualized):
[[0.03041, -0.009272, 0.007789, 0.007123], [-0.009272, 0.347793, 0.006634, -0.001526], [0.007789, 0.006634, 0.010368, 0.004981], [0.007123, -0.001526, 0.004981, 0.015645]]
Risk-free rate: 4.00%
Constraints: weights 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_ETH-USD=0.1098, w_HAUZ=0.8902, w_TLT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLV=0.0000, w_ETH-USD=0.1098, w_HAUZ=0.8902, w_TLT=0.0000
Portfolio annualized return: 49.12%, volatility: 11.71%
Sharpe ratio: (0.4912 - 0.0400) / 0.1171 = 3.8538


4-asset optimization. Max-Sharpe: 2.973. Portfolio: return=8.31%, vol=1.45%. Weights: w_QUAL=0.0000, w_BNB-USD=0.0145, w_DBA=0.0000, w_SHY=0.9855.

Question:
Assets: QUAL, BNB-USD, DBA, SHY
Annualized mean returns: QUAL:-0.9987, BNB-USD:0.0295, DBA:-0.3068, SHY:0.0839
Covariance matrix (annualized):
[[0.052062, 0.028894, 0.016178, -0.001395], [0.028894, 0.175141, 0.031483, -0.002622], [0.016178, 0.031483, 0.029163, -0.000593], [-0.001395, -0.002622, -0.000593, 0.000255]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bear

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

Answer: w_QUAL=0.0000, w_BNB-USD=0.0145, w_DBA=0.0000, w_SHY=0.9855

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QUAL=0.0000, w_BNB-USD=0.0145, w_DBA=0.0000, w_SHY=0.9855
Portfolio annualized return: 8.31%, volatility: 1.45%
Sharpe ratio: (0.0831 - 0.0400) / 0.0145 = 2.9735


4-asset optimization. Max-Sharpe: 0.713. Portfolio: return=4.42%, vol=0.58%. Weights: w_VTI=0.0000, w_SOL-USD=0.0001, w_INDS=0.0000, w_ICSH=0.9999.

Question:
Assets: VTI, SOL-USD, INDS, ICSH
Annualized mean returns: VTI:-0.6349, SOL-USD:0.1577, INDS:-0.3244, ICSH:0.0442
Covariance matrix (annualized):
[[0.066641, 0.12064, 0.044325, 0.000255], [0.12064, 0.953645, 0.050971, 0.000914], [0.044325, 0.050971, 0.072114, 0.000509], [0.000255, 0.000914, 0.000509, 3.4e-05]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bear

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

Answer: w_VTI=0.0000, w_SOL-USD=0.0001, w_INDS=0.0000, w_ICSH=0.9999

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_VTI=0.0000, w_SOL-USD=0.0001, w_INDS=0.0000, w_ICSH=0.9999
Portfolio annualized return: 4.42%, volatility: 0.58%
Sharpe ratio: (0.0442 - 0.0400) / 0.0058 = 0.7133


4-asset optimization. Max-Sharpe: 3.369. Portfolio: return=84.08%, vol=23.77%. Weights: w_XLY=0.0000, w_AVAX-USD=0.2140, w_CSHI=0.0000, w_HAUZ=0.7860.

Question:
Assets: XLY, AVAX-USD, CSHI, HAUZ
Annualized mean returns: XLY:0.2160, AVAX-USD:2.2293, CSHI:0.0567, HAUZ:0.4628
Covariance matrix (annualized):
[[0.095587, 0.102193, 0.008622, 0.021448], [0.102193, 0.632046, 0.015149, 0.024377], [0.008622, 0.015149, 0.002094, 0.004964], [0.021448, 0.024377, 0.004964, 0.031302]]
Risk-free rate: 4.00%
Constraints: weights 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_AVAX-USD=0.2140, w_CSHI=0.0000, w_HAUZ=0.7860

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLY=0.0000, w_AVAX-USD=0.2140, w_CSHI=0.0000, w_HAUZ=0.7860
Portfolio annualized return: 84.08%, volatility: 23.77%
Sharpe ratio: (0.8408 - 0.0400) / 0.2377 = 3.3694


4-asset optimization. Max-Sharpe: 2.856. Portfolio: return=4.85%, vol=0.30%. Weights: w_EEM=0.0000, w_BTC-USD=0.0039, w_BIL=0.9961, w_TLT=0.0000.

Question:
Assets: EEM, BTC-USD, BIL, TLT
Annualized mean returns: EEM:0.0982, BTC-USD:0.8574, BIL:0.0453, TLT:-0.3360
Covariance matrix (annualized):
[[0.021059, 0.0196, -6e-06, 0.002904], [0.0196, 0.175614, 0.00016, 0.020782], [-6e-06, 0.00016, 5e-06, -1e-05], [0.002904, 0.020782, -1e-05, 0.013858]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_EEM=0.0000, w_BTC-USD=0.0039, w_BIL=0.9961, w_TLT=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_EEM=0.0000, w_BTC-USD=0.0039, w_BIL=0.9961, w_TLT=0.0000
Portfolio annualized return: 4.85%, volatility: 0.30%
Sharpe ratio: (0.0485 - 0.0400) / 0.0030 = 2.8559


4-asset optimization. Max-Sharpe: 2.832. Portfolio: return=39.86%, vol=12.66%. Weights: w_^VIX=0.0977, w_ADA-USD=0.0368, w_WEAT=0.2599, w_SCHH=0.6055.

Question:
Assets: ^VIX, ADA-USD, WEAT, SCHH
Annualized mean returns: ^VIX:1.7718, ADA-USD:-0.0455, WEAT:0.1724, SCHH:0.3011
Covariance matrix (annualized):
[[1.233037, -0.273164, -0.051388, -0.032387], [-0.273164, 0.609242, -0.030297, 0.0137], [-0.051388, -0.030297, 0.060578, -0.006086], [-0.032387, 0.0137, -0.006086, 0.026293]]
Risk-free rate: 4.00%
Constraints: weights 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=0.0977, w_ADA-USD=0.0368, w_WEAT=0.2599, w_SCHH=0.6055

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_^VIX=0.0977, w_ADA-USD=0.0368, w_WEAT=0.2599, w_SCHH=0.6055
Portfolio annualized return: 39.86%, volatility: 12.66%
Sharpe ratio: (0.3986 - 0.0400) / 0.1266 = 2.8316


4-asset optimization. Max-Sharpe: 4.289. Portfolio: return=11.57%, vol=1.76%. Weights: w_QQQ=0.0000, w_BTC-USD=0.0000, w_REZ=0.0293, w_TIP=0.9707.

Question:
Assets: QQQ, BTC-USD, REZ, TIP
Annualized mean returns: QQQ:-0.5269, BTC-USD:-0.7827, REZ:0.3127, TIP:0.1097
Covariance matrix (annualized):
[[0.055376, 0.040133, 0.004306, -0.00083], [0.040133, 0.200807, -0.007299, -0.00227], [0.004306, -0.007299, 0.031706, 0.000198], [-0.00083, -0.00227, 0.000198, 0.00029]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: sideways

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

Answer: w_QQQ=0.0000, w_BTC-USD=0.0000, w_REZ=0.0293, w_TIP=0.9707

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_QQQ=0.0000, w_BTC-USD=0.0000, w_REZ=0.0293, w_TIP=0.9707
Portfolio annualized return: 11.57%, volatility: 1.76%
Sharpe ratio: (0.1157 - 0.0400) / 0.0176 = 4.2886


4-asset optimization. Max-Sharpe: 3.173. Portfolio: return=50.42%, vol=14.63%. Weights: w_XLE=0.4400, w_XRP-USD=0.1082, w_TLH=0.4518, w_HAUZ=0.0000.

Question:
Assets: XLE, XRP-USD, TLH, HAUZ
Annualized mean returns: XLE:0.4823, XRP-USD:1.8937, TLH:0.1926, HAUZ:0.1219
Covariance matrix (annualized):
[[0.037964, 0.030567, 0.000842, 0.004445], [0.030567, 0.589699, 0.018107, 0.021043], [0.000842, 0.018107, 0.010411, 0.007005], [0.004445, 0.021043, 0.007005, 0.013359]]
Risk-free rate: 4.00%
Constraints: weights 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=0.4400, w_XRP-USD=0.1082, w_TLH=0.4518, w_HAUZ=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLE=0.4400, w_XRP-USD=0.1082, w_TLH=0.4518, w_HAUZ=0.0000
Portfolio annualized return: 50.42%, volatility: 14.63%
Sharpe ratio: (0.5042 - 0.0400) / 0.1463 = 3.1731


4-asset optimization. Max-Sharpe: 7.121. Portfolio: return=9.80%, vol=0.81%. Weights: w_XLI=0.0500, w_AVAX-USD=0.0000, w_ICSH=0.9274, w_SLV=0.0226.

Question:
Assets: XLI, AVAX-USD, ICSH, SLV
Annualized mean returns: XLI:0.5470, AVAX-USD:-0.5441, ICSH:0.0531, SLV:0.9486
Covariance matrix (annualized):
[[0.011185, 0.014038, 0.000138, -0.004757], [0.014038, 0.462482, 0.000449, 0.016533], [0.000138, 0.000449, 1e-05, -3.5e-05], [-0.004757, 0.016533, -3.5e-05, 0.058041]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_XLI=0.0500, w_AVAX-USD=0.0000, w_ICSH=0.9274, w_SLV=0.0226

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLI=0.0500, w_AVAX-USD=0.0000, w_ICSH=0.9274, w_SLV=0.0226
Portfolio annualized return: 9.80%, volatility: 0.81%
Sharpe ratio: (0.0980 - 0.0400) / 0.0081 = 7.1205


4-asset optimization. Max-Sharpe: 3.112. Portfolio: return=33.82%, vol=9.58%. Weights: w_ACWI=1.0000, w_BTC-USD=0.0000, w_VNQ=0.0000, w_PALL=0.0000.

Question:
Assets: ACWI, BTC-USD, VNQ, PALL
Annualized mean returns: ACWI:0.3382, BTC-USD:-0.1265, VNQ:0.1613, PALL:-0.3407
Covariance matrix (annualized):
[[0.009181, 0.014145, 0.00595, -0.001496], [0.014145, 0.073814, 0.010085, 0.021845], [0.00595, 0.010085, 0.022038, 0.004585], [-0.001496, 0.021845, 0.004585, 0.087786]]
Risk-free rate: 4.00%
Constraints: weights sum to 1, all weights ≥ 0
Market regime: bull

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

Answer: w_ACWI=1.0000, w_BTC-USD=0.0000, w_VNQ=0.0000, w_PALL=0.0000

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_ACWI=1.0000, w_BTC-USD=0.0000, w_VNQ=0.0000, w_PALL=0.0000
Portfolio annualized return: 33.82%, volatility: 9.58%
Sharpe ratio: (0.3382 - 0.0400) / 0.0958 = 3.1121


4-asset optimization. Max-Sharpe: 2.727. Portfolio: return=48.76%, vol=16.42%. Weights: w_XLK=0.0000, w_SOL-USD=0.1939, w_PPLT=0.6759, w_IEF=0.1302.

Question:
Assets: XLK, SOL-USD, PPLT, IEF
Annualized mean returns: XLK:0.2069, SOL-USD:1.2084, PPLT:0.3632, IEF:0.0607
Covariance matrix (annualized):
[[0.047442, 0.026975, 0.008665, 0.00167], [0.026975, 0.374212, -0.004914, 0.008557], [0.008665, -0.004914, 0.030452, -0.001328], [0.00167, 0.008557, -0.001328, 0.003709]]
Risk-free rate: 4.00%
Constraints: weights 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_SOL-USD=0.1939, w_PPLT=0.6759, w_IEF=0.1302

Explanation:
Solved max-Sharpe via SLSQP numerical optimization.
Optimal weights: w_XLK=0.0000, w_SOL-USD=0.1939, w_PPLT=0.6759, w_IEF=0.1302
Portfolio annualized return: 48.76%, volatility: 16.42%
Sharpe ratio: (0.4876 - 0.0400) / 0.1642 = 2.7268