Question:
Assets: QUAL, ICSH
QUAL: annualized_mean_return=0.0504, daily_std=0.0074
ICSH: annualized_mean_return=0.0756, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0739
Market regime: sideways

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

Answer: w_QUAL=0.0018, w_ICSH=0.9982

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000055 + 0.000000 - 0.000000)
  Unconstrained: w_QUAL=0.0011
  After long-only clamp: w_QUAL=0.0011, w_ICSH=0.9989.


Question:
Assets: ETH-USD, VNQ
ETH-USD: annualized_mean_return=-0.0756, daily_std=0.0209
VNQ: annualized_mean_return=0.3276, daily_std=0.0112
Minimum required portfolio return (annualized): 0.3001
Market regime: sideways

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

Answer: w_ETH-USD=0.0682, w_VNQ=0.9318

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000125 - 0.000001) / (0.000437 + 0.000125 - 0.000003)
  Unconstrained: w_ETH-USD=0.2209
  After long-only clamp: w_ETH-USD=0.2209, w_VNQ=0.7791.


MATIC-USD σ=0.0458, CPER σ=0.0102, ρ=0.010. Min-variance weights: MATIC-USD=0.045, CPER=0.955.

Question:
Assets: MATIC-USD, CPER
MATIC-USD: annualized_mean_return=0.2520, daily_std=0.0458
CPER: annualized_mean_return=0.1260, daily_std=0.0102
Minimum required portfolio return (annualized): 0.1311
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_CPER) 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_CPER=X.XXXX

Answer: w_MATIC-USD=0.0449, w_CPER=0.9551

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000103 - 0.000005) / (0.002095 + 0.000103 - 0.000009)
  Unconstrained: w_MATIC-USD=0.0450
  After long-only clamp: w_MATIC-USD=0.0450, w_CPER=0.9550.


Question:
Assets: VTI, ICSH
VTI: annualized_mean_return=0.3780, daily_std=0.0061
ICSH: annualized_mean_return=0.0756, daily_std=0.0002
Minimum required portfolio return (annualized): 0.1969
Market regime: sideways

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=0.4011, w_ICSH=0.5989

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000037 + 0.000000 - -0.000000)
  Unconstrained: w_VTI=0.0032
  After long-only clamp: w_VTI=0.0032, w_ICSH=0.9968.


Question:
Assets: ETH-USD, FXI
ETH-USD: annualized_mean_return=1.1844, daily_std=0.0279
FXI: annualized_mean_return=-0.4788, daily_std=0.0184
Minimum required portfolio return (annualized): 0.3192
Market regime: sideways

Compute portfolio weights (w_ETH-USD, w_FXI) 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_FXI=X.XXXX

Answer: w_ETH-USD=0.4798, w_FXI=0.5202

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000337 - 0.000036) / (0.000776 + 0.000337 - 0.000071)
  Unconstrained: w_ETH-USD=0.2894
  After long-only clamp: w_ETH-USD=0.2894, w_FXI=0.7106.


Question:
Assets: ETH-USD, VNQ
ETH-USD: annualized_mean_return=0.9072, daily_std=0.0264
VNQ: annualized_mean_return=-0.0504, daily_std=0.0131
Minimum required portfolio return (annualized): 0.0911
Market regime: sideways

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

Answer: w_ETH-USD=0.1567, w_VNQ=0.8433

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000173 - 0.000053) / (0.000698 + 0.000173 - 0.000106)
  Unconstrained: w_ETH-USD=0.1568
  After long-only clamp: w_ETH-USD=0.1568, w_VNQ=0.8432.


Question:
Assets: FXI, LINK-USD
FXI: annualized_mean_return=0.8568, daily_std=0.0189
LINK-USD: annualized_mean_return=0.2772, daily_std=0.0329
Minimum required portfolio return (annualized): 0.7513
Market regime: sideways

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

Answer: w_FXI=0.8180, w_LINK-USD=0.1820

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.001080 - -0.000067) / (0.000356 + 0.001080 - -0.000135)
  Unconstrained: w_FXI=0.7306
  After long-only clamp: w_FXI=0.7306, w_LINK-USD=0.2694.


Question:
Assets: VTI, SHY
VTI: annualized_mean_return=0.2268, daily_std=0.0067
SHY: annualized_mean_return=-0.0000, daily_std=0.0012
Minimum required portfolio return (annualized): -0.0000
Market regime: sideways

Compute portfolio weights (w_VTI, w_SHY) 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_SHY=X.XXXX

Answer: w_VTI=0.0000, w_SHY=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - 0.000002) / (0.000045 + 0.000001 - 0.000003)
  Unconstrained: w_VTI=-0.0073
  After long-only clamp: w_VTI=0.0000, w_SHY=1.0000.


Question:
Assets: MTUM, GLD
MTUM: annualized_mean_return=-0.0504, daily_std=0.0095
GLD: annualized_mean_return=0.2268, daily_std=0.0100
Minimum required portfolio return (annualized): 0.1146
Market regime: sideways

Compute portfolio weights (w_MTUM, w_GLD) 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_GLD=X.XXXX

Answer: w_MTUM=0.4048, w_GLD=0.5952

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000099 - -0.000018) / (0.000090 + 0.000099 - -0.000037)
  Unconstrained: w_MTUM=0.5200
  After long-only clamp: w_MTUM=0.5200, w_GLD=0.4800.


Question:
Assets: VEA, BIL
VEA: annualized_mean_return=-0.0000, daily_std=0.0095
BIL: annualized_mean_return=0.0756, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0625
Market regime: sideways

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

Answer: w_VEA=0.0003, w_BIL=0.9997

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000090 + 0.000000 - 0.000000)
  Unconstrained: w_VEA=-0.0005
  After long-only clamp: w_VEA=0.0000, w_BIL=1.0000.


Question:
Assets: VTI, IAU
VTI: annualized_mean_return=0.4032, daily_std=0.0077
IAU: annualized_mean_return=-0.0756, daily_std=0.0080
Minimum required portfolio return (annualized): 0.2661
Market regime: sideways

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

Answer: w_VTI=0.7137, w_IAU=0.2863

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000065 - 0.000013) / (0.000059 + 0.000065 - 0.000026)
  Unconstrained: w_VTI=0.5293
  After long-only clamp: w_VTI=0.5293, w_IAU=0.4707.


Question:
Assets: XLP, IAU
XLP: annualized_mean_return=0.1008, daily_std=0.0069
IAU: annualized_mean_return=0.1764, daily_std=0.0102
Minimum required portfolio return (annualized): 0.1181
Market regime: sideways

Compute portfolio weights (w_XLP, w_IAU) 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_IAU=X.XXXX

Answer: w_XLP=0.7073, w_IAU=0.2927

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000104 - 0.000008) / (0.000048 + 0.000104 - 0.000015)
  Unconstrained: w_XLP=0.7065
  After long-only clamp: w_XLP=0.7065, w_IAU=0.2935.


Question:
Assets: IWM, ITB
IWM: annualized_mean_return=-0.1008, daily_std=0.0158
ITB: annualized_mean_return=0.2016, daily_std=0.0196
Minimum required portfolio return (annualized): -0.0994
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=0.9946, w_ITB=0.0054

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000384 - 0.000249) / (0.000250 + 0.000384 - 0.000498)
  Unconstrained: w_IWM=0.9940
  After long-only clamp: w_IWM=0.9940, w_ITB=0.0060.


Question:
Assets: VEA, MORT
VEA: annualized_mean_return=-0.1764, daily_std=0.0072
MORT: annualized_mean_return=-0.1512, daily_std=0.0087
Minimum required portfolio return (annualized): -0.1705
Market regime: bull

Compute portfolio weights (w_VEA, w_MORT) 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_MORT=X.XXXX

Answer: w_VEA=0.6698, w_MORT=0.3302

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000076 - 0.000027) / (0.000051 + 0.000076 - 0.000055)
  Unconstrained: w_VEA=0.6719
  After long-only clamp: w_VEA=0.6719, w_MORT=0.3281.


LINK-USD σ=0.0424, INDS σ=0.0107, ρ=-0.052. Min-variance weights: LINK-USD=0.070, INDS=0.930.

Question:
Assets: LINK-USD, INDS
LINK-USD: annualized_mean_return=0.5796, daily_std=0.0424
INDS: annualized_mean_return=-0.2016, daily_std=0.0107
Minimum required portfolio return (annualized): 0.0878
Market regime: sideways

Compute portfolio weights (w_LINK-USD, w_INDS) 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_INDS=X.XXXX

Answer: w_LINK-USD=0.3705, w_INDS=0.6295

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000114 - -0.000024) / (0.001802 + 0.000114 - -0.000047)
  Unconstrained: w_LINK-USD=0.0700
  After long-only clamp: w_LINK-USD=0.0700, w_INDS=0.9300.


Question:
Assets: BNB-USD, USO
BNB-USD: annualized_mean_return=-0.9324, daily_std=0.0256
USO: annualized_mean_return=0.2016, daily_std=0.0208
Minimum required portfolio return (annualized): -0.3831
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_USO) 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_USO=X.XXXX

Answer: w_BNB-USD=0.3877, w_USO=0.6123

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000432 - 0.000050) / (0.000653 + 0.000432 - 0.000101)
  Unconstrained: w_BNB-USD=0.3876
  After long-only clamp: w_BNB-USD=0.3876, w_USO=0.6124.


Question:
Assets: XLY, IYR
XLY: annualized_mean_return=0.6552, daily_std=0.0111
IYR: annualized_mean_return=0.3780, daily_std=0.0110
Minimum required portfolio return (annualized): 0.4581
Market regime: sideways

Compute portfolio weights (w_XLY, w_IYR) 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_IYR=X.XXXX

Answer: w_XLY=0.4913, w_IYR=0.5087

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000120 - 0.000065) / (0.000122 + 0.000120 - 0.000129)
  Unconstrained: w_XLY=0.4914
  After long-only clamp: w_XLY=0.4914, w_IYR=0.5086.


Question:
Assets: SOL-USD, CORN
SOL-USD: annualized_mean_return=1.3608, daily_std=0.0459
CORN: annualized_mean_return=0.4788, daily_std=0.0198
Minimum required portfolio return (annualized): 1.1776
Market regime: sideways

Compute portfolio weights (w_SOL-USD, w_CORN) 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_CORN=X.XXXX

Answer: w_SOL-USD=0.7923, w_CORN=0.2077

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000394 - -0.000229) / (0.002108 + 0.000394 - -0.000458)
  Unconstrained: w_SOL-USD=0.2103
  After long-only clamp: w_SOL-USD=0.2103, w_CORN=0.7897.


AVAX-USD σ=0.0602, VNQ σ=0.0135, ρ=0.140. Min-variance weights: AVAX-USD=0.019, VNQ=0.981.

Question:
Assets: AVAX-USD, VNQ
AVAX-USD: annualized_mean_return=6.9048, daily_std=0.0602
VNQ: annualized_mean_return=0.6048, daily_std=0.0135
Minimum required portfolio return (annualized): 0.6582
Market regime: sideways

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

Answer: w_AVAX-USD=0.0191, w_VNQ=0.9809

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000183 - 0.000114) / (0.003630 + 0.000183 - 0.000228)
  Unconstrained: w_AVAX-USD=0.0192
  After long-only clamp: w_AVAX-USD=0.0192, w_VNQ=0.9808.


Question:
Assets: XLK, CSHI
XLK: annualized_mean_return=0.4032, daily_std=0.0118
CSHI: annualized_mean_return=0.0756, daily_std=0.0005
Minimum required portfolio return (annualized): 0.2091
Market regime: sideways

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

Answer: w_XLK=0.4075, w_CSHI=0.5925

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000138 + 0.000000 - 0.000000)
  Unconstrained: w_XLK=0.0018
  After long-only clamp: w_XLK=0.0018, w_CSHI=0.9982.


Question:
Assets: USMV, ICSH
USMV: annualized_mean_return=0.2520, daily_std=0.0042
ICSH: annualized_mean_return=0.0252, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0260
Market regime: bull

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

Answer: w_USMV=0.0040, w_ICSH=0.9960

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000018 + 0.000000 - -0.000000)
  Unconstrained: w_USMV=0.0091
  After long-only clamp: w_USMV=0.0091, w_ICSH=0.9909.


Question:
Assets: XLB, CSHI
XLB: annualized_mean_return=-0.4788, daily_std=0.0080
CSHI: annualized_mean_return=0.0756, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0752
Market regime: sideways

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

Answer: w_XLB=0.0007, w_CSHI=0.9993

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000065 + 0.000000 - -0.000000)
  Unconstrained: w_XLB=0.0053
  After long-only clamp: w_XLB=0.0053, w_CSHI=0.9947.


Question:
Assets: AVAX-USD, VNQ
AVAX-USD: annualized_mean_return=2.4696, daily_std=0.0555
VNQ: annualized_mean_return=0.5796, daily_std=0.0128
Minimum required portfolio return (annualized): 2.0541
Market regime: sideways

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

Answer: w_AVAX-USD=0.7802, w_VNQ=0.2198

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000164 - -0.000091) / (0.003077 + 0.000164 - -0.000182)
  Unconstrained: w_AVAX-USD=0.0746
  After long-only clamp: w_AVAX-USD=0.0746, w_VNQ=0.9254.


Question:
Assets: IWM, SGOV
IWM: annualized_mean_return=0.4284, daily_std=0.0118
SGOV: annualized_mean_return=0.0756, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0757
Market regime: sideways

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) / (0.000138 + 0.000000 - -0.000001)
  Unconstrained: w_IWM=0.0026
  After long-only clamp: w_IWM=0.0026, w_SGOV=0.9974.


Question:
Assets: XLF, BNDX
XLF: annualized_mean_return=-0.3276, daily_std=0.0141
BNDX: annualized_mean_return=0.0756, daily_std=0.0036
Minimum required portfolio return (annualized): 0.0584
Market regime: sideways

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

Answer: w_XLF=0.0427, w_BNDX=0.9573

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000013 - -0.000007) / (0.000198 + 0.000013 - -0.000013)
  Unconstrained: w_XLF=0.0876
  After long-only clamp: w_XLF=0.0876, w_BNDX=0.9124.


XRP-USD σ=0.0191, SOYB σ=0.0080, ρ=0.063. Min-variance weights: XRP-USD=0.133, SOYB=0.867.

Question:
Assets: XRP-USD, SOYB
XRP-USD: annualized_mean_return=-0.3528, daily_std=0.0191
SOYB: annualized_mean_return=-0.1512, daily_std=0.0080
Minimum required portfolio return (annualized): -0.2224
Market regime: bull

Compute portfolio weights (w_XRP-USD, w_SOYB) 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_SOYB=X.XXXX

Answer: w_XRP-USD=0.1321, w_SOYB=0.8679

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000064 - 0.000010) / (0.000366 + 0.000064 - 0.000019)
  Unconstrained: w_XRP-USD=0.1326
  After long-only clamp: w_XRP-USD=0.1326, w_SOYB=0.8674.


AVAX-USD σ=0.0596, EWJ σ=0.0098, ρ=0.061. Min-variance weights: AVAX-USD=0.017, EWJ=0.983.

Question:
Assets: AVAX-USD, EWJ
AVAX-USD: annualized_mean_return=6.6528, daily_std=0.0596
EWJ: annualized_mean_return=0.1008, daily_std=0.0098
Minimum required portfolio return (annualized): 2.7864
Market regime: sideways

Compute portfolio weights (w_AVAX-USD, w_EWJ) 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_EWJ=X.XXXX

Answer: w_AVAX-USD=0.4099, w_EWJ=0.5901

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000095 - 0.000036) / (0.003556 + 0.000095 - 0.000071)
  Unconstrained: w_AVAX-USD=0.0167
  After long-only clamp: w_AVAX-USD=0.0167, w_EWJ=0.9833.


Question:
Assets: QUAL, ICSH
QUAL: annualized_mean_return=0.0756, daily_std=0.0074
ICSH: annualized_mean_return=0.0504, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0643
Market regime: sideways

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

Answer: w_QUAL=0.5516, w_ICSH=0.4484

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000054 + 0.000000 - 0.000001)
  Unconstrained: w_QUAL=-0.0063
  After long-only clamp: w_QUAL=0.0000, w_ICSH=1.0000.


Question:
Assets: EEM, XRP-USD
EEM: annualized_mean_return=-0.0252, daily_std=0.0095
XRP-USD: annualized_mean_return=0.9828, daily_std=0.0282
Minimum required portfolio return (annualized): 0.7774
Market regime: sideways

Compute portfolio weights (w_EEM, w_XRP-USD) 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_XRP-USD=X.XXXX

Answer: w_EEM=0.2038, w_XRP-USD=0.7962

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000795 - 0.000020) / (0.000090 + 0.000795 - 0.000040)
  Unconstrained: w_EEM=0.9172
  After long-only clamp: w_EEM=0.9172, w_XRP-USD=0.0828.


Question:
Assets: USMV, REZ
USMV: annualized_mean_return=0.1764, daily_std=0.0088
REZ: annualized_mean_return=0.4536, daily_std=0.0145
Minimum required portfolio return (annualized): 0.1764
Market regime: sideways

Compute portfolio weights (w_USMV, w_REZ) 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_REZ=X.XXXX

Answer: w_USMV=1.0000, w_REZ=0.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000209 - 0.000093) / (0.000078 + 0.000209 - 0.000187)
  Unconstrained: w_USMV=1.1534
  After long-only clamp: w_USMV=1.0000, w_REZ=0.0000.


Question:
Assets: XLY, IEF
XLY: annualized_mean_return=0.8064, daily_std=0.0104
IEF: annualized_mean_return=-0.1008, daily_std=0.0038
Minimum required portfolio return (annualized): 0.2628
Market regime: bull

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

Answer: w_XLY=0.4008, w_IEF=0.5992

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000015 - 0.000005) / (0.000108 + 0.000015 - 0.000009)
  Unconstrained: w_XLY=0.0896
  After long-only clamp: w_XLY=0.0896, w_IEF=0.9104.


Question:
Assets: IVV, ITB
IVV: annualized_mean_return=0.2772, daily_std=0.0073
ITB: annualized_mean_return=0.8064, daily_std=0.0130
Minimum required portfolio return (annualized): 0.2816
Market regime: sideways

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

Answer: w_IVV=0.9871, w_ITB=0.0129

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000168 - 0.000052) / (0.000054 + 0.000168 - 0.000105)
  Unconstrained: w_IVV=0.9899
  After long-only clamp: w_IVV=0.9899, w_ITB=0.0101.


Question:
Assets: XLU, DBA
XLU: annualized_mean_return=0.5040, daily_std=0.0082
DBA: annualized_mean_return=0.3528, daily_std=0.0098
Minimum required portfolio return (annualized): 0.4052
Market regime: sideways

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

Answer: w_XLU=0.5862, w_DBA=0.4138

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000096 - -0.000004) / (0.000067 + 0.000096 - -0.000008)
  Unconstrained: w_XLU=0.5863
  After long-only clamp: w_XLU=0.5863, w_DBA=0.4137.


Question:
Assets: ADA-USD, VNQ
ADA-USD: annualized_mean_return=-0.0504, daily_std=0.0326
VNQ: annualized_mean_return=0.4788, daily_std=0.0088
Minimum required portfolio return (annualized): 0.4698
Market regime: bull

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

Answer: w_ADA-USD=0.0170, w_VNQ=0.9830

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000077 - 0.000035) / (0.001062 + 0.000077 - 0.000071)
  Unconstrained: w_ADA-USD=0.0385
  After long-only clamp: w_ADA-USD=0.0385, w_VNQ=0.9615.


AVAX-USD σ=0.0524, BIL σ=0.0002, ρ=0.062. Min-variance weights: AVAX-USD=0.000, BIL=1.000.

Question:
Assets: AVAX-USD, BIL
AVAX-USD: annualized_mean_return=-1.7892, daily_std=0.0524
BIL: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): -0.2786
Market regime: bull

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

Answer: w_AVAX-USD=0.0000, w_BIL=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.002747 + 0.000000 - 0.000001)
  Unconstrained: w_AVAX-USD=-0.0002
  After long-only clamp: w_AVAX-USD=0.0000, w_BIL=1.0000.


MATIC-USD σ=0.0373, BIL σ=0.0002, ρ=0.052. Min-variance weights: MATIC-USD=0.000, BIL=1.000.

Question:
Assets: MATIC-USD, BIL
MATIC-USD: annualized_mean_return=2.3688, daily_std=0.0373
BIL: annualized_mean_return=0.0252, daily_std=0.0002
Minimum required portfolio return (annualized): 0.7988
Market regime: sideways

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

Answer: w_MATIC-USD=0.3301, w_BIL=0.6699

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.001388 + 0.000000 - 0.000001)
  Unconstrained: w_MATIC-USD=-0.0002
  After long-only clamp: w_MATIC-USD=0.0000, w_BIL=1.0000.


Question:
Assets: VEA, INDS
VEA: annualized_mean_return=0.1512, daily_std=0.0091
INDS: annualized_mean_return=-0.0000, daily_std=0.0119
Minimum required portfolio return (annualized): 0.0576
Market regime: sideways

Compute portfolio weights (w_VEA, w_INDS) 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_INDS=X.XXXX

Answer: w_VEA=0.7953, w_INDS=0.2047

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000142 - 0.000062) / (0.000083 + 0.000142 - 0.000124)
  Unconstrained: w_VEA=0.7941
  After long-only clamp: w_VEA=0.7941, w_INDS=0.2059.


ADA-USD σ=0.0510, ICSH σ=0.0003, ρ=0.246. Min-variance weights: ADA-USD=0.000, ICSH=1.000.

Question:
Assets: ADA-USD, ICSH
ADA-USD: annualized_mean_return=3.4272, daily_std=0.0510
ICSH: annualized_mean_return=0.0504, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0504
Market regime: sideways

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 - 0.000003) / (0.002605 + 0.000000 - 0.000007)
  Unconstrained: w_ADA-USD=-0.0013
  After long-only clamp: w_ADA-USD=0.0000, w_ICSH=1.0000.


BNB-USD σ=0.0147, ICSH σ=0.0003, ρ=0.037. Min-variance weights: BNB-USD=0.000, ICSH=1.000.

Question:
Assets: BNB-USD, ICSH
BNB-USD: annualized_mean_return=-0.5292, daily_std=0.0147
ICSH: annualized_mean_return=0.0504, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0503
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=0.0002, w_ICSH=0.9998

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000217 + 0.000000 - 0.000000)
  Unconstrained: w_BNB-USD=-0.0003
  After long-only clamp: w_BNB-USD=0.0000, w_ICSH=1.0000.


Question:
Assets: QUAL, BTC-USD
QUAL: annualized_mean_return=0.4032, daily_std=0.0123
BTC-USD: annualized_mean_return=1.3356, daily_std=0.0205
Minimum required portfolio return (annualized): 0.6170
Market regime: sideways

Compute portfolio weights (w_QUAL, w_BTC-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_BTC-USD=X.XXXX

Answer: w_QUAL=0.7356, w_BTC-USD=0.2644

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000420 - -0.000001) / (0.000150 + 0.000420 - -0.000003)
  Unconstrained: w_QUAL=0.7352
  After long-only clamp: w_QUAL=0.7352, w_BTC-USD=0.2648.


Question:
Assets: XRP-USD, ITB
XRP-USD: annualized_mean_return=0.9576, daily_std=0.0334
ITB: annualized_mean_return=0.5040, daily_std=0.0176
Minimum required portfolio return (annualized): 0.5656
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_ITB) 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_ITB=X.XXXX

Answer: w_XRP-USD=0.2004, w_ITB=0.7996

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000311 - 0.000041) / (0.001119 + 0.000311 - 0.000081)
  Unconstrained: w_XRP-USD=0.2005
  After long-only clamp: w_XRP-USD=0.2005, w_ITB=0.7995.


MATIC-USD σ=0.0388, IAU σ=0.0103, ρ=-0.293. Min-variance weights: MATIC-USD=0.121, IAU=0.879.

Question:
Assets: MATIC-USD, IAU
MATIC-USD: annualized_mean_return=-0.7056, daily_std=0.0388
IAU: annualized_mean_return=0.3528, daily_std=0.0103
Minimum required portfolio return (annualized): 0.3180
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_IAU) 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_IAU=X.XXXX

Answer: w_MATIC-USD=0.0329, w_IAU=0.9671

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000106 - -0.000117) / (0.001502 + 0.000106 - -0.000234)
  Unconstrained: w_MATIC-USD=0.1209
  After long-only clamp: w_MATIC-USD=0.1209, w_IAU=0.8791.


Question:
Assets: ^VIX, SHV
^VIX: annualized_mean_return=-1.0584, daily_std=0.0547
SHV: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0503
Market regime: sideways

Compute portfolio weights (w_^VIX, w_SHV) 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_SHV=X.XXXX

Answer: w_^VIX=0.0001, w_SHV=0.9999

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000001) / (0.002995 + 0.000000 - -0.000003)
  Unconstrained: w_^VIX=0.0005
  After long-only clamp: w_^VIX=0.0005, w_SHV=0.9995.


Question:
Assets: XRP-USD, TIP
XRP-USD: annualized_mean_return=0.7560, daily_std=0.0272
TIP: annualized_mean_return=0.0504, daily_std=0.0016
Minimum required portfolio return (annualized): 0.2418
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_TIP) 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_TIP=X.XXXX

Answer: w_XRP-USD=0.2713, w_TIP=0.7287

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000003 - -0.000001) / (0.000742 + 0.000003 - -0.000001)
  Unconstrained: w_XRP-USD=0.0042
  After long-only clamp: w_XRP-USD=0.0042, w_TIP=0.9958.


Question:
Assets: MTUM, BIL
MTUM: annualized_mean_return=0.4284, daily_std=0.0085
BIL: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0504
Market regime: sideways

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

Answer: w_MTUM=0.0002, w_BIL=0.9998

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000072 + 0.000000 - 0.000000)
  Unconstrained: w_MTUM=-0.0008
  After long-only clamp: w_MTUM=0.0000, w_BIL=1.0000.


Question:
Assets: QUAL, SCHH
QUAL: annualized_mean_return=0.5040, daily_std=0.0077
SCHH: annualized_mean_return=-0.1008, daily_std=0.0103
Minimum required portfolio return (annualized): 0.2539
Market regime: sideways

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

Answer: w_QUAL=0.7459, w_SCHH=0.2541

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000107 - 0.000034) / (0.000059 + 0.000107 - 0.000068)
  Unconstrained: w_QUAL=0.7459
  After long-only clamp: w_QUAL=0.7459, w_SCHH=0.2541.


Question:
Assets: IVV, INDS
IVV: annualized_mean_return=0.1008, daily_std=0.0102
INDS: annualized_mean_return=0.5292, daily_std=0.0105
Minimum required portfolio return (annualized): 0.3923
Market regime: sideways

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

Answer: w_IVV=0.3196, w_INDS=0.6804

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000111 - 0.000056) / (0.000103 + 0.000111 - 0.000111)
  Unconstrained: w_IVV=0.5360
  After long-only clamp: w_IVV=0.5360, w_INDS=0.4640.


Question:
Assets: FXI, ICSH
FXI: annualized_mean_return=-0.3024, daily_std=0.0181
ICSH: annualized_mean_return=0.0504, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0063
Market regime: sideways

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

Answer: w_FXI=0.0003, w_ICSH=0.9997

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000329 + 0.000000 - 0.000001)
  Unconstrained: w_FXI=-0.0012
  After long-only clamp: w_FXI=0.0000, w_ICSH=1.0000.


LINK-USD σ=0.0364, VCIT σ=0.0033, ρ=0.167. Min-variance weights: LINK-USD=0.000, VCIT=1.000.

Question:
Assets: LINK-USD, VCIT
LINK-USD: annualized_mean_return=-1.3356, daily_std=0.0364
VCIT: annualized_mean_return=0.1764, daily_std=0.0033
Minimum required portfolio return (annualized): -0.5876
Market regime: sideways

Compute portfolio weights (w_LINK-USD, w_VCIT) 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_VCIT=X.XXXX

Answer: w_LINK-USD=0.0000, w_VCIT=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000011 - 0.000020) / (0.001325 + 0.000011 - 0.000040)
  Unconstrained: w_LINK-USD=-0.0071
  After long-only clamp: w_LINK-USD=0.0000, w_VCIT=1.0000.


Question:
Assets: XRP-USD, GLD
XRP-USD: annualized_mean_return=0.1008, daily_std=0.0242
GLD: annualized_mean_return=-0.2268, daily_std=0.0075
Minimum required portfolio return (annualized): -0.2167
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_GLD) 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_GLD=X.XXXX

Answer: w_XRP-USD=0.0686, w_GLD=0.9314

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000057 - 0.000015) / (0.000584 + 0.000057 - 0.000030)
  Unconstrained: w_XRP-USD=0.0687
  After long-only clamp: w_XRP-USD=0.0687, w_GLD=0.9313.


Question:
Assets: SOL-USD, MORT
SOL-USD: annualized_mean_return=0.9072, daily_std=0.0472
MORT: annualized_mean_return=0.8568, daily_std=0.0150
Minimum required portfolio return (annualized): 0.8963
Market regime: sideways

Compute portfolio weights (w_SOL-USD, w_MORT) 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_MORT=X.XXXX

Answer: w_SOL-USD=0.7837, w_MORT=0.2163

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000226 - -0.000064) / (0.002227 + 0.000226 - -0.000127)
  Unconstrained: w_SOL-USD=0.1122
  After long-only clamp: w_SOL-USD=0.1122, w_MORT=0.8878.


Question:
Assets: XLU, CSHI
XLU: annualized_mean_return=-0.1512, daily_std=0.0092
CSHI: annualized_mean_return=0.0756, daily_std=0.0005
Minimum required portfolio return (annualized): 0.0272
Market regime: sideways

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

Answer: w_XLU=0.0147, w_CSHI=0.9853

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000001) / (0.000085 + 0.000000 - -0.000001)
  Unconstrained: w_XLU=0.0106
  After long-only clamp: w_XLU=0.0106, w_CSHI=0.9894.


Question:
Assets: XLV, ICSH
XLV: annualized_mean_return=0.2520, daily_std=0.0077
ICSH: annualized_mean_return=0.0756, daily_std=0.0003
Minimum required portfolio return (annualized): 0.1994
Market regime: sideways

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

Answer: w_XLV=0.7018, w_ICSH=0.2982

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.000060 + 0.000000 - 0.000001)
  Unconstrained: w_XLV=-0.0099
  After long-only clamp: w_XLV=0.0000, w_ICSH=1.0000.


XLI σ=0.0097, LINK-USD σ=0.0333, ρ=0.022. Min-variance weights: XLI=0.927, LINK-USD=0.073.

Question:
Assets: XLI, LINK-USD
XLI: annualized_mean_return=0.4032, daily_std=0.0097
LINK-USD: annualized_mean_return=0.6552, daily_std=0.0333
Minimum required portfolio return (annualized): 0.4203
Market regime: sideways

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=0.9270, w_LINK-USD=0.0730

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.001112 - 0.000007) / (0.000094 + 0.001112 - 0.000014)
  Unconstrained: w_XLI=0.9272
  After long-only clamp: w_XLI=0.9272, w_LINK-USD=0.0728.


MATIC-USD σ=0.0401, ICSH σ=0.0003, ρ=-0.025. Min-variance weights: MATIC-USD=0.000, ICSH=1.000.

Question:
Assets: MATIC-USD, ICSH
MATIC-USD: annualized_mean_return=0.4536, daily_std=0.0401
ICSH: annualized_mean_return=0.0504, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0504
Market regime: sideways

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

Answer: w_MATIC-USD=0.0001, w_ICSH=0.9999

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.001606 + 0.000000 - -0.000001)
  Unconstrained: w_MATIC-USD=0.0003
  After long-only clamp: w_MATIC-USD=0.0003, w_ICSH=0.9997.


Question:
Assets: EWJ, PALL
EWJ: annualized_mean_return=0.1260, daily_std=0.0084
PALL: annualized_mean_return=0.1512, daily_std=0.0235
Minimum required portfolio return (annualized): 0.1383
Market regime: sideways

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

Answer: w_EWJ=0.5119, w_PALL=0.4881

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000550 - 0.000015) / (0.000070 + 0.000550 - 0.000029)
  Unconstrained: w_EWJ=0.9062
  After long-only clamp: w_EWJ=0.9062, w_PALL=0.0938.


Question:
Assets: ETH-USD, DBB
ETH-USD: annualized_mean_return=0.1008, daily_std=0.0279
DBB: annualized_mean_return=0.4032, daily_std=0.0127
Minimum required portfolio return (annualized): 0.2336
Market regime: sideways

Compute portfolio weights (w_ETH-USD, w_DBB) 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_DBB=X.XXXX

Answer: w_ETH-USD=0.1819, w_DBB=0.8181

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000161 - -0.000016) / (0.000780 + 0.000161 - -0.000033)
  Unconstrained: w_ETH-USD=0.1822
  After long-only clamp: w_ETH-USD=0.1822, w_DBB=0.8178.


Question:
Assets: QQQ, WEAT
QQQ: annualized_mean_return=0.5544, daily_std=0.0096
WEAT: annualized_mean_return=-0.3780, daily_std=0.0118
Minimum required portfolio return (annualized): 0.1026
Market regime: bull

Compute portfolio weights (w_QQQ, w_WEAT) 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_WEAT=X.XXXX

Answer: w_QQQ=0.6117, w_WEAT=0.3883

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000140 - 0.000011) / (0.000093 + 0.000140 - 0.000022)
  Unconstrained: w_QQQ=0.6115
  After long-only clamp: w_QQQ=0.6115, w_WEAT=0.3885.


Question:
Assets: BNB-USD, IGOV
BNB-USD: annualized_mean_return=1.2096, daily_std=0.0250
IGOV: annualized_mean_return=0.0756, daily_std=0.0072
Minimum required portfolio return (annualized): 1.0041
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_IGOV) 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_IGOV=X.XXXX

Answer: w_BNB-USD=0.8188, w_IGOV=0.1812

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000052 - -0.000056) / (0.000627 + 0.000052 - -0.000113)
  Unconstrained: w_BNB-USD=0.1366
  After long-only clamp: w_BNB-USD=0.1366, w_IGOV=0.8634.


Question:
Assets: EEM, JNK
EEM: annualized_mean_return=0.3276, daily_std=0.0096
JNK: annualized_mean_return=0.3276, daily_std=0.0042
Minimum required portfolio return (annualized): 0.3276
Market regime: sideways

Compute portfolio weights (w_EEM, w_JNK) 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_JNK=X.XXXX

Answer: w_EEM=0.1569, w_JNK=0.8431

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000018 - 0.000001) / (0.000092 + 0.000018 - 0.000001)
  Unconstrained: w_EEM=0.1592
  After long-only clamp: w_EEM=0.1592, w_JNK=0.8408.


Question:
Assets: BNB-USD, DBC
BNB-USD: annualized_mean_return=2.7720, daily_std=0.0435
DBC: annualized_mean_return=0.3024, daily_std=0.0065
Minimum required portfolio return (annualized): 2.0654
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_DBC) 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_DBC=X.XXXX

Answer: w_BNB-USD=0.7139, w_DBC=0.2861

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000043 - -0.000014) / (0.001896 + 0.000043 - -0.000028)
  Unconstrained: w_BNB-USD=0.0289
  After long-only clamp: w_BNB-USD=0.0289, w_DBC=0.9711.


DOT-USD σ=0.0525, MORT σ=0.0174, ρ=0.094. Min-variance weights: DOT-USD=0.075, MORT=0.925.

Question:
Assets: DOT-USD, MORT
DOT-USD: annualized_mean_return=1.8396, daily_std=0.0525
MORT: annualized_mean_return=0.5040, daily_std=0.0174
Minimum required portfolio return (annualized): 1.5257
Market regime: sideways

Compute portfolio weights (w_DOT-USD, w_MORT) 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_MORT=X.XXXX

Answer: w_DOT-USD=0.7650, w_MORT=0.2350

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000302 - 0.000086) / (0.002760 + 0.000302 - 0.000172)
  Unconstrained: w_DOT-USD=0.0746
  After long-only clamp: w_DOT-USD=0.0746, w_MORT=0.9254.


Question:
Assets: BTC-USD, SLV
BTC-USD: annualized_mean_return=0.1260, daily_std=0.0245
SLV: annualized_mean_return=-0.1260, daily_std=0.0144
Minimum required portfolio return (annualized): -0.0952
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_SLV) 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_SLV=X.XXXX

Answer: w_BTC-USD=0.2760, w_SLV=0.7240

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000207 - -0.000034) / (0.000598 + 0.000207 - -0.000068)
  Unconstrained: w_BTC-USD=0.2759
  After long-only clamp: w_BTC-USD=0.2759, w_SLV=0.7241.


Question:
Assets: XLE, ETH-USD
XLE: annualized_mean_return=0.0000, daily_std=0.0100
ETH-USD: annualized_mean_return=-0.4284, daily_std=0.0243
Minimum required portfolio return (annualized): -0.0363
Market regime: sideways

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

Answer: w_XLE=0.9153, w_ETH-USD=0.0847

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000589 - -0.000026) / (0.000101 + 0.000589 - -0.000051)
  Unconstrained: w_XLE=0.8293
  After long-only clamp: w_XLE=0.8293, w_ETH-USD=0.1707.


Question:
Assets: XRP-USD, TIP
XRP-USD: annualized_mean_return=-0.5292, daily_std=0.0229
TIP: annualized_mean_return=0.1008, daily_std=0.0010
Minimum required portfolio return (annualized): 0.0969
Market regime: bull

Compute portfolio weights (w_XRP-USD, w_TIP) 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_TIP=X.XXXX

Answer: w_XRP-USD=0.0062, w_TIP=0.9938

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - -0.000004) / (0.000524 + 0.000001 - -0.000009)
  Unconstrained: w_XRP-USD=0.0102
  After long-only clamp: w_XRP-USD=0.0102, w_TIP=0.9898.


MATIC-USD σ=0.0273, XHB σ=0.0160, ρ=0.244. Min-variance weights: MATIC-USD=0.190, XHB=0.810.

Question:
Assets: MATIC-USD, XHB
MATIC-USD: annualized_mean_return=-1.4112, daily_std=0.0273
XHB: annualized_mean_return=0.2016, daily_std=0.0160
Minimum required portfolio return (annualized): 0.0997
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_XHB) 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_XHB=X.XXXX

Answer: w_MATIC-USD=0.0632, w_XHB=0.9368

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000257 - 0.000107) / (0.000746 + 0.000257 - 0.000214)
  Unconstrained: w_MATIC-USD=0.1901
  After long-only clamp: w_MATIC-USD=0.1901, w_XHB=0.8099.


Question:
Assets: XLY, XHB
XLY: annualized_mean_return=0.0756, daily_std=0.0097
XHB: annualized_mean_return=0.5544, daily_std=0.0128
Minimum required portfolio return (annualized): 0.1125
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=0.8856, w_XHB=0.1144

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000164 - 0.000083) / (0.000094 + 0.000164 - 0.000165)
  Unconstrained: w_XLY=0.8829
  After long-only clamp: w_XLY=0.8829, w_XHB=0.1171.


Question:
Assets: XRP-USD, VNQ
XRP-USD: annualized_mean_return=0.8820, daily_std=0.0433
VNQ: annualized_mean_return=-0.0756, daily_std=0.0146
Minimum required portfolio return (annualized): 0.3623
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=0.4573, w_VNQ=0.5427

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000214 - -0.000081) / (0.001878 + 0.000214 - -0.000161)
  Unconstrained: w_XRP-USD=0.1309
  After long-only clamp: w_XRP-USD=0.1309, w_VNQ=0.8691.


Question:
Assets: ACWI, UNG
ACWI: annualized_mean_return=0.3024, daily_std=0.0082
UNG: annualized_mean_return=-1.1592, daily_std=0.0368
Minimum required portfolio return (annualized): -0.2424
Market regime: sideways

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

Answer: w_ACWI=0.9868, w_UNG=0.0132

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.001357 - 0.000050) / (0.000067 + 0.001357 - 0.000100)
  Unconstrained: w_ACWI=0.9867
  After long-only clamp: w_ACWI=0.9867, w_UNG=0.0133.


MATIC-USD σ=0.0376, CSHI σ=0.0004, ρ=0.062. Min-variance weights: MATIC-USD=0.000, CSHI=1.000.

Question:
Assets: MATIC-USD, CSHI
MATIC-USD: annualized_mean_return=1.4112, daily_std=0.0376
CSHI: annualized_mean_return=0.0504, daily_std=0.0004
Minimum required portfolio return (annualized): 0.0504
Market regime: sideways

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

Answer: w_MATIC-USD=0.0000, w_CSHI=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.001412 + 0.000000 - 0.000002)
  Unconstrained: w_MATIC-USD=-0.0005
  After long-only clamp: w_MATIC-USD=0.0000, w_CSHI=1.0000.


MATIC-USD σ=0.0386, SHY σ=0.0011, ρ=0.192. Min-variance weights: MATIC-USD=0.000, SHY=1.000.

Question:
Assets: MATIC-USD, SHY
MATIC-USD: annualized_mean_return=0.0756, daily_std=0.0386
SHY: annualized_mean_return=0.0756, daily_std=0.0011
Minimum required portfolio return (annualized): 0.0756
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_SHY) 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_SHY=X.XXXX

Answer: w_MATIC-USD=0.0000, w_SHY=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - 0.000008) / (0.001486 + 0.000001 - 0.000016)
  Unconstrained: w_MATIC-USD=-0.0046
  After long-only clamp: w_MATIC-USD=0.0000, w_SHY=1.0000.


AVAX-USD σ=0.0668, XLU σ=0.0103, ρ=0.075. Min-variance weights: AVAX-USD=0.012, XLU=0.988.

Question:
Assets: AVAX-USD, XLU
AVAX-USD: annualized_mean_return=4.8888, daily_std=0.0668
XLU: annualized_mean_return=0.3024, daily_std=0.0103
Minimum required portfolio return (annualized): 2.5818
Market regime: sideways

Compute portfolio weights (w_AVAX-USD, w_XLU) 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_XLU=X.XXXX

Answer: w_AVAX-USD=0.4970, w_XLU=0.5030

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000107 - 0.000052) / (0.004457 + 0.000107 - 0.000103)
  Unconstrained: w_AVAX-USD=0.0124
  After long-only clamp: w_AVAX-USD=0.0124, w_XLU=0.9876.


Question:
Assets: XLF, CSHI
XLF: annualized_mean_return=-0.1512, daily_std=0.0074
CSHI: annualized_mean_return=0.1008, daily_std=0.0006
Minimum required portfolio return (annualized): 0.0187
Market regime: sideways

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=0.0064, w_CSHI=0.9936

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000055 + 0.000000 - 0.000001)
  Unconstrained: w_XLF=0.0002
  After long-only clamp: w_XLF=0.0002, w_CSHI=0.9998.


Question:
Assets: BTC-USD, CPER
BTC-USD: annualized_mean_return=-0.0252, daily_std=0.0242
CPER: annualized_mean_return=0.1764, daily_std=0.0153
Minimum required portfolio return (annualized): 0.1576
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_CPER) 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_CPER=X.XXXX

Answer: w_BTC-USD=0.0933, w_CPER=0.9067

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000234 - -0.000028) / (0.000585 + 0.000234 - -0.000055)
  Unconstrained: w_BTC-USD=0.2994
  After long-only clamp: w_BTC-USD=0.2994, w_CPER=0.7006.


Question:
Assets: ADA-USD, VNQ
ADA-USD: annualized_mean_return=-0.1764, daily_std=0.0354
VNQ: annualized_mean_return=-0.1260, daily_std=0.0139
Minimum required portfolio return (annualized): -0.1431
Market regime: sideways

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

Answer: w_ADA-USD=0.0865, w_VNQ=0.9135

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000194 - 0.000083) / (0.001254 + 0.000194 - 0.000166)
  Unconstrained: w_ADA-USD=0.0865
  After long-only clamp: w_ADA-USD=0.0865, w_VNQ=0.9135.


Question:
Assets: EWJ, IGOV
EWJ: annualized_mean_return=-0.0756, daily_std=0.0094
IGOV: annualized_mean_return=-0.0504, daily_std=0.0050
Minimum required portfolio return (annualized): -0.0506
Market regime: bull

Compute portfolio weights (w_EWJ, w_IGOV) 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_IGOV=X.XXXX

Answer: w_EWJ=0.0079, w_IGOV=0.9921

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000025 - 0.000023) / (0.000088 + 0.000025 - 0.000046)
  Unconstrained: w_EWJ=0.0260
  After long-only clamp: w_EWJ=0.0260, w_IGOV=0.9740.


SOL-USD σ=0.0330, SOYB σ=0.0116, ρ=0.028. Min-variance weights: SOL-USD=0.104, SOYB=0.896.

Question:
Assets: SOL-USD, SOYB
SOL-USD: annualized_mean_return=-0.3780, daily_std=0.0330
SOYB: annualized_mean_return=0.0504, daily_std=0.0116
Minimum required portfolio return (annualized): 0.0177
Market regime: sideways

Compute portfolio weights (w_SOL-USD, w_SOYB) 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_SOYB=X.XXXX

Answer: w_SOL-USD=0.0763, w_SOYB=0.9237

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000135 - 0.000011) / (0.001088 + 0.000135 - 0.000022)
  Unconstrained: w_SOL-USD=0.1036
  After long-only clamp: w_SOL-USD=0.1036, w_SOYB=0.8964.


Question:
Assets: LINK-USD, BIL
LINK-USD: annualized_mean_return=1.1088, daily_std=0.0389
BIL: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.3867
Market regime: bull

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

Answer: w_LINK-USD=0.3177, w_BIL=0.6823

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.001516 + 0.000000 - -0.000001)
  Unconstrained: w_LINK-USD=0.0002
  After long-only clamp: w_LINK-USD=0.0002, w_BIL=0.9998.


Question:
Assets: XLE, SCHH
XLE: annualized_mean_return=-0.2016, daily_std=0.0171
SCHH: annualized_mean_return=-0.3276, daily_std=0.0132
Minimum required portfolio return (annualized): -0.2894
Market regime: sideways

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

Answer: w_XLE=0.3436, w_SCHH=0.6564

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000173 - 0.000041) / (0.000294 + 0.000173 - 0.000082)
  Unconstrained: w_XLE=0.3435
  After long-only clamp: w_XLE=0.3435, w_SCHH=0.6565.


Question:
Assets: ETH-USD, SHY
ETH-USD: annualized_mean_return=0.1260, daily_std=0.0278
SHY: annualized_mean_return=0.0756, daily_std=0.0013
Minimum required portfolio return (annualized): 0.1055
Market regime: sideways

Compute portfolio weights (w_ETH-USD, w_SHY) 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_SHY=X.XXXX

Answer: w_ETH-USD=0.5933, w_SHY=0.4067

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000002 - 0.000003) / (0.000775 + 0.000002 - 0.000007)
  Unconstrained: w_ETH-USD=-0.0023
  After long-only clamp: w_ETH-USD=0.0000, w_SHY=1.0000.


Question:
Assets: BTC-USD, DBB
BTC-USD: annualized_mean_return=-0.6552, daily_std=0.0172
DBB: annualized_mean_return=0.1008, daily_std=0.0107
Minimum required portfolio return (annualized): -0.4253
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_DBB) 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_DBB=X.XXXX

Answer: w_BTC-USD=0.2815, w_DBB=0.7185

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000114 - -0.000003) / (0.000295 + 0.000114 - -0.000007)
  Unconstrained: w_BTC-USD=0.2818
  After long-only clamp: w_BTC-USD=0.2818, w_DBB=0.7182.


Question:
Assets: XLB, SCHH
XLB: annualized_mean_return=-0.3024, daily_std=0.0077
SCHH: annualized_mean_return=-0.2268, daily_std=0.0084
Minimum required portfolio return (annualized): -0.2464
Market regime: bull

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

Answer: w_XLB=0.2593, w_SCHH=0.7407

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000071 - 0.000017) / (0.000059 + 0.000071 - 0.000034)
  Unconstrained: w_XLB=0.5607
  After long-only clamp: w_XLB=0.5607, w_SCHH=0.4393.


Question:
Assets: XLK, REZ
XLK: annualized_mean_return=0.5040, daily_std=0.0111
REZ: annualized_mean_return=-0.0504, daily_std=0.0106
Minimum required portfolio return (annualized): 0.0822
Market regime: bull

Compute portfolio weights (w_XLK, w_REZ) 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_REZ=X.XXXX

Answer: w_XLK=0.4705, w_REZ=0.5295

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000112 - 0.000026) / (0.000123 + 0.000112 - 0.000053)
  Unconstrained: w_XLK=0.4704
  After long-only clamp: w_XLK=0.4704, w_REZ=0.5296.


BTC-USD σ=0.0286, WEAT σ=0.0109, ρ=0.028. Min-variance weights: BTC-USD=0.120, WEAT=0.879.

Question:
Assets: BTC-USD, WEAT
BTC-USD: annualized_mean_return=1.6128, daily_std=0.0286
WEAT: annualized_mean_return=-0.5544, daily_std=0.0109
Minimum required portfolio return (annualized): 0.9388
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=0.6890, w_WEAT=0.3110

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000120 - 0.000009) / (0.000818 + 0.000120 - 0.000018)
  Unconstrained: w_BTC-USD=0.1205
  After long-only clamp: w_BTC-USD=0.1205, w_WEAT=0.8795.


Question:
Assets: VLUE, INDS
VLUE: annualized_mean_return=0.2772, daily_std=0.0075
INDS: annualized_mean_return=-0.1008, daily_std=0.0099
Minimum required portfolio return (annualized): 0.1080
Market regime: sideways

Compute portfolio weights (w_VLUE, w_INDS) 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_INDS=X.XXXX

Answer: w_VLUE=0.8194, w_INDS=0.1806

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000098 - 0.000045) / (0.000057 + 0.000098 - 0.000089)
  Unconstrained: w_VLUE=0.8156
  After long-only clamp: w_VLUE=0.8156, w_INDS=0.1844.


Question:
Assets: QQQ, BNB-USD
QQQ: annualized_mean_return=-0.1008, daily_std=0.0148
BNB-USD: annualized_mean_return=0.1008, daily_std=0.0294
Minimum required portfolio return (annualized): -0.0740
Market regime: sideways

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

Answer: w_QQQ=0.8152, w_BNB-USD=0.1848

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000865 - 0.000028) / (0.000218 + 0.000865 - 0.000057)
  Unconstrained: w_QQQ=0.8154
  After long-only clamp: w_QQQ=0.8154, w_BNB-USD=0.1846.


Question:
Assets: XLY, SHY
XLY: annualized_mean_return=0.2772, daily_std=0.0146
SHY: annualized_mean_return=0.1260, daily_std=0.0010
Minimum required portfolio return (annualized): 0.2319
Market regime: sideways

Compute portfolio weights (w_XLY, w_SHY) 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_SHY=X.XXXX

Answer: w_XLY=0.7004, w_SHY=0.2996

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - 0.000001) / (0.000213 + 0.000001 - 0.000002)
  Unconstrained: w_XLY=-0.0011
  After long-only clamp: w_XLY=0.0000, w_SHY=1.0000.


Question:
Assets: IWM, TLH
IWM: annualized_mean_return=0.1260, daily_std=0.0117
TLH: annualized_mean_return=-0.2520, daily_std=0.0066
Minimum required portfolio return (annualized): -0.1556
Market regime: sideways

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

Answer: w_IWM=0.2675, w_TLH=0.7325

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000044 - -0.000009) / (0.000136 + 0.000044 - -0.000018)
  Unconstrained: w_IWM=0.2679
  After long-only clamp: w_IWM=0.2679, w_TLH=0.7321.


Question:
Assets: XLP, BIL
XLP: annualized_mean_return=-0.4788, daily_std=0.0066
BIL: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): -0.0494
Market regime: sideways

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

Answer: w_XLP=0.0005, w_BIL=0.9995

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000043 + 0.000000 - 0.000000)
  Unconstrained: w_XLP=-0.0019
  After long-only clamp: w_XLP=0.0000, w_BIL=1.0000.


Question:
Assets: XLV, TLT
XLV: annualized_mean_return=-0.1764, daily_std=0.0068
TLT: annualized_mean_return=-0.1512, daily_std=0.0086
Minimum required portfolio return (annualized): -0.1614
Market regime: bull

Compute portfolio weights (w_XLV, w_TLT) 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_TLT=X.XXXX

Answer: w_XLV=0.4048, w_TLT=0.5952

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000073 - 0.000011) / (0.000046 + 0.000073 - 0.000021)
  Unconstrained: w_XLV=0.6379
  After long-only clamp: w_XLV=0.6379, w_TLT=0.3621.


Question:
Assets: XLRE, ETH-USD
XLRE: annualized_mean_return=0.1764, daily_std=0.0135
ETH-USD: annualized_mean_return=1.4616, daily_std=0.0259
Minimum required portfolio return (annualized): 0.3440
Market regime: sideways

Compute portfolio weights (w_XLRE, w_ETH-USD) 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_ETH-USD=X.XXXX

Answer: w_XLRE=0.7773, w_ETH-USD=0.2227

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000673 - -0.000015) / (0.000182 + 0.000673 - -0.000029)
  Unconstrained: w_XLRE=0.7776
  After long-only clamp: w_XLRE=0.7776, w_ETH-USD=0.2224.


Question:
Assets: ETH-USD, IEF
ETH-USD: annualized_mean_return=2.0664, daily_std=0.0325
IEF: annualized_mean_return=-0.0252, daily_std=0.0042
Minimum required portfolio return (annualized): 0.7199
Market regime: bull

Compute portfolio weights (w_ETH-USD, w_IEF) 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_IEF=X.XXXX

Answer: w_ETH-USD=0.3562, w_IEF=0.6438

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000017 - 0.000006) / (0.001054 + 0.000017 - 0.000012)
  Unconstrained: w_ETH-USD=0.0106
  After long-only clamp: w_ETH-USD=0.0106, w_IEF=0.9894.


Question:
Assets: MTUM, CSHI
MTUM: annualized_mean_return=0.2016, daily_std=0.0103
CSHI: annualized_mean_return=0.0756, daily_std=0.0003
Minimum required portfolio return (annualized): 0.1352
Market regime: sideways

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

Answer: w_MTUM=0.4730, w_CSHI=0.5270

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000106 + 0.000000 - -0.000000)
  Unconstrained: w_MTUM=0.0012
  After long-only clamp: w_MTUM=0.0012, w_CSHI=0.9988.


Question:
Assets: AVAX-USD, SHY
AVAX-USD: annualized_mean_return=-0.7560, daily_std=0.0509
SHY: annualized_mean_return=0.0252, daily_std=0.0010
Minimum required portfolio return (annualized): -0.3986
Market regime: bull

Compute portfolio weights (w_AVAX-USD, w_SHY) 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_SHY=X.XXXX

Answer: w_AVAX-USD=0.0011, w_SHY=0.9989

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - -0.000002) / (0.002590 + 0.000001 - -0.000003)
  Unconstrained: w_AVAX-USD=0.0010
  After long-only clamp: w_AVAX-USD=0.0010, w_SHY=0.9990.


ETH-USD σ=0.0369, BNDX σ=0.0025, ρ=0.015. Min-variance weights: ETH-USD=0.004, BNDX=0.996.

Question:
Assets: ETH-USD, BNDX
ETH-USD: annualized_mean_return=-0.9072, daily_std=0.0369
BNDX: annualized_mean_return=0.0504, daily_std=0.0025
Minimum required portfolio return (annualized): 0.0487
Market regime: sideways

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

Answer: w_ETH-USD=0.0018, w_BNDX=0.9982

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000006 - 0.000001) / (0.001362 + 0.000006 - 0.000003)
  Unconstrained: w_ETH-USD=0.0037
  After long-only clamp: w_ETH-USD=0.0037, w_BNDX=0.9963.


Question:
Assets: BNB-USD, VTI
BNB-USD: annualized_mean_return=-1.1592, daily_std=0.0262
VTI: annualized_mean_return=0.4788, daily_std=0.0081
Minimum required portfolio return (annualized): 0.4526
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_VTI) 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_VTI=X.XXXX

Answer: w_BNB-USD=0.0160, w_VTI=0.9840

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000065 - 0.000016) / (0.000686 + 0.000065 - 0.000033)
  Unconstrained: w_BNB-USD=0.0680
  After long-only clamp: w_BNB-USD=0.0680, w_VTI=0.9320.


Question:
Assets: SOL-USD, UNG
SOL-USD: annualized_mean_return=0.3276, daily_std=0.0402
UNG: annualized_mean_return=0.7560, daily_std=0.0305
Minimum required portfolio return (annualized): 0.5220
Market regime: sideways

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

Answer: w_SOL-USD=0.3627, w_UNG=0.6373

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000931 - 0.000023) / (0.001619 + 0.000931 - 0.000046)
  Unconstrained: w_SOL-USD=0.3627
  After long-only clamp: w_SOL-USD=0.3627, w_UNG=0.6373.


Question:
Assets: VTI, GLD
VTI: annualized_mean_return=0.4032, daily_std=0.0082
GLD: annualized_mean_return=0.4536, daily_std=0.0081
Minimum required portfolio return (annualized): 0.4344
Market regime: sideways

Compute portfolio weights (w_VTI, w_GLD) 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_GLD=X.XXXX

Answer: w_VTI=0.3810, w_GLD=0.6190

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000066 - 0.000025) / (0.000067 + 0.000066 - 0.000049)
  Unconstrained: w_VTI=0.4927
  After long-only clamp: w_VTI=0.4927, w_GLD=0.5073.


Question:
Assets: IWM, HAUZ
IWM: annualized_mean_return=0.1764, daily_std=0.0146
HAUZ: annualized_mean_return=0.1764, daily_std=0.0100
Minimum required portfolio return (annualized): 0.1763
Market regime: bull

Compute portfolio weights (w_IWM, w_HAUZ) 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_HAUZ=X.XXXX

Answer: w_IWM=0.0614, w_HAUZ=0.9386

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000101 - 0.000093) / (0.000213 + 0.000101 - 0.000186)
  Unconstrained: w_IWM=0.0601
  After long-only clamp: w_IWM=0.0601, w_HAUZ=0.9399.


AVAX-USD σ=0.0270, CSHI σ=0.0005, ρ=-0.136. Min-variance weights: AVAX-USD=0.003, CSHI=0.997.

Question:
Assets: AVAX-USD, CSHI
AVAX-USD: annualized_mean_return=0.4284, daily_std=0.0270
CSHI: annualized_mean_return=0.0756, daily_std=0.0005
Minimum required portfolio return (annualized): 0.0762
Market regime: sideways

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

Answer: w_AVAX-USD=0.0031, w_CSHI=0.9969

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000002) / (0.000727 + 0.000000 - -0.000004)
  Unconstrained: w_AVAX-USD=0.0029
  After long-only clamp: w_AVAX-USD=0.0029, w_CSHI=0.9971.


Question:
Assets: IVV, CSHI
IVV: annualized_mean_return=0.0504, daily_std=0.0082
CSHI: annualized_mean_return=0.0504, daily_std=0.0005
Minimum required portfolio return (annualized): 0.0504
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=0.0041, w_CSHI=0.9959

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000067 + 0.000000 - -0.000001)
  Unconstrained: w_IVV=0.0085
  After long-only clamp: w_IVV=0.0085, w_CSHI=0.9915.


Question:
Assets: EFA, SOYB
EFA: annualized_mean_return=0.2016, daily_std=0.0085
SOYB: annualized_mean_return=-0.0252, daily_std=0.0098
Minimum required portfolio return (annualized): 0.1608
Market regime: sideways

Compute portfolio weights (w_EFA, w_SOYB) 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_SOYB=X.XXXX

Answer: w_EFA=0.8201, w_SOYB=0.1799

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000096 - 0.000009) / (0.000073 + 0.000096 - 0.000017)
  Unconstrained: w_EFA=0.5756
  After long-only clamp: w_EFA=0.5756, w_SOYB=0.4244.


Question:
Assets: FXI, MORT
FXI: annualized_mean_return=-0.5040, daily_std=0.0167
MORT: annualized_mean_return=-0.8820, daily_std=0.0172
Minimum required portfolio return (annualized): -0.6236
Market regime: sideways

Compute portfolio weights (w_FXI, w_MORT) 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_MORT=X.XXXX

Answer: w_FXI=0.6836, w_MORT=0.3164

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000297 - 0.000055) / (0.000279 + 0.000297 - 0.000109)
  Unconstrained: w_FXI=0.5193
  After long-only clamp: w_FXI=0.5193, w_MORT=0.4807.


Question:
Assets: EFA, BIL
EFA: annualized_mean_return=0.1260, daily_std=0.0077
BIL: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0680
Market regime: sideways

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

Answer: w_EFA=0.2328, w_BIL=0.7672

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000060 + 0.000000 - 0.000000)
  Unconstrained: w_EFA=-0.0011
  After long-only clamp: w_EFA=0.0000, w_BIL=1.0000.


Question:
Assets: IWM, HYG
IWM: annualized_mean_return=0.1512, daily_std=0.0131
HYG: annualized_mean_return=0.1260, daily_std=0.0063
Minimum required portfolio return (annualized): 0.1393
Market regime: sideways

Compute portfolio weights (w_IWM, w_HYG) 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_HYG=X.XXXX

Answer: w_IWM=0.5278, w_HYG=0.4722

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000040 - 0.000005) / (0.000171 + 0.000040 - 0.000009)
  Unconstrained: w_IWM=0.1753
  After long-only clamp: w_IWM=0.1753, w_HYG=0.8247.


Question:
Assets: EEM, SGOV
EEM: annualized_mean_return=0.1008, daily_std=0.0090
SGOV: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0755
Market regime: sideways

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

Answer: w_EEM=0.4980, w_SGOV=0.5020

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000082 + 0.000000 - 0.000000)
  Unconstrained: w_EEM=-0.0007
  After long-only clamp: w_EEM=0.0000, w_SGOV=1.0000.


Question:
Assets: DOT-USD, JNK
DOT-USD: annualized_mean_return=-0.6048, daily_std=0.0390
JNK: annualized_mean_return=0.0504, daily_std=0.0032
Minimum required portfolio return (annualized): 0.0489
Market regime: sideways

Compute portfolio weights (w_DOT-USD, w_JNK) 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_JNK=X.XXXX

Answer: w_DOT-USD=0.0023, w_JNK=0.9977

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000010 - 0.000006) / (0.001518 + 0.000010 - 0.000013)
  Unconstrained: w_DOT-USD=0.0027
  After long-only clamp: w_DOT-USD=0.0027, w_JNK=0.9973.


Question:
Assets: ETH-USD, SGOV
ETH-USD: annualized_mean_return=-0.9324, daily_std=0.0234
SGOV: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0504
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) / (0.000546 + 0.000000 - -0.000000)
  Unconstrained: w_ETH-USD=0.0001
  After long-only clamp: w_ETH-USD=0.0001, w_SGOV=0.9999.


Question:
Assets: XLI, ITB
XLI: annualized_mean_return=0.1512, daily_std=0.0103
ITB: annualized_mean_return=0.5796, daily_std=0.0160
Minimum required portfolio return (annualized): 0.4617
Market regime: sideways

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

Answer: w_XLI=0.2752, w_ITB=0.7248

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000257 - 0.000116) / (0.000107 + 0.000257 - 0.000233)
  Unconstrained: w_XLI=1.0744
  After long-only clamp: w_XLI=1.0000, w_ITB=0.0000.


Question:
Assets: MTUM, ICSH
MTUM: annualized_mean_return=0.7056, daily_std=0.0117
ICSH: annualized_mean_return=0.0504, daily_std=0.0003
Minimum required portfolio return (annualized): 0.2962
Market regime: sideways

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

Answer: w_MTUM=0.3752, w_ICSH=0.6248

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000137 + 0.000000 - 0.000000)
  Unconstrained: w_MTUM=-0.0003
  After long-only clamp: w_MTUM=0.0000, w_ICSH=1.0000.


LINK-USD σ=0.0455, PALL σ=0.0213, ρ=0.230. Min-variance weights: LINK-USD=0.112, PALL=0.888.

Question:
Assets: LINK-USD, PALL
LINK-USD: annualized_mean_return=-0.5040, daily_std=0.0455
PALL: annualized_mean_return=-0.0756, daily_std=0.0213
Minimum required portfolio return (annualized): -0.1099
Market regime: bull

Compute portfolio weights (w_LINK-USD, w_PALL) 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_PALL=X.XXXX

Answer: w_LINK-USD=0.0801, w_PALL=0.9199

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000455 - 0.000223) / (0.002068 + 0.000455 - 0.000445)
  Unconstrained: w_LINK-USD=0.1117
  After long-only clamp: w_LINK-USD=0.1117, w_PALL=0.8883.


Question:
Assets: XLE, CORN
XLE: annualized_mean_return=-0.2520, daily_std=0.0107
CORN: annualized_mean_return=-0.3780, daily_std=0.0114
Minimum required portfolio return (annualized): -0.3365
Market regime: sideways

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

Answer: w_XLE=0.5243, w_CORN=0.4757

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000130 - -0.000024) / (0.000115 + 0.000130 - -0.000047)
  Unconstrained: w_XLE=0.5244
  After long-only clamp: w_XLE=0.5244, w_CORN=0.4756.


Question:
Assets: EWJ, CPER
EWJ: annualized_mean_return=0.2772, daily_std=0.0086
CPER: annualized_mean_return=-0.2268, daily_std=0.0128
Minimum required portfolio return (annualized): 0.0382
Market regime: sideways

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

Answer: w_EWJ=0.7209, w_CPER=0.2791

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000164 - 0.000017) / (0.000074 + 0.000164 - 0.000034)
  Unconstrained: w_EWJ=0.7212
  After long-only clamp: w_EWJ=0.7212, w_CPER=0.2788.


Question:
Assets: SOL-USD, FXI
SOL-USD: annualized_mean_return=0.9324, daily_std=0.0493
FXI: annualized_mean_return=-0.0756, daily_std=0.0126
Minimum required portfolio return (annualized): -0.0581
Market regime: bull

Compute portfolio weights (w_SOL-USD, w_FXI) 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_FXI=X.XXXX

Answer: w_SOL-USD=0.0282, w_FXI=0.9718

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000160 - 0.000092) / (0.002431 + 0.000160 - 0.000183)
  Unconstrained: w_SOL-USD=0.0283
  After long-only clamp: w_SOL-USD=0.0283, w_FXI=0.9717.


ADA-USD σ=0.0489, WEAT σ=0.0147, ρ=0.028. Min-variance weights: ADA-USD=0.076, WEAT=0.924.

Question:
Assets: ADA-USD, WEAT
ADA-USD: annualized_mean_return=1.6380, daily_std=0.0489
WEAT: annualized_mean_return=0.1008, daily_std=0.0147
Minimum required portfolio return (annualized): 0.1733
Market regime: sideways

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

Answer: w_ADA-USD=0.0761, w_WEAT=0.9239

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000215 - 0.000020) / (0.002391 + 0.000215 - 0.000040)
  Unconstrained: w_ADA-USD=0.0760
  After long-only clamp: w_ADA-USD=0.0760, w_WEAT=0.9240.


Question:
Assets: DOT-USD, IWM
DOT-USD: annualized_mean_return=-1.5120, daily_std=0.0386
IWM: annualized_mean_return=0.0000, daily_std=0.0141
Minimum required portfolio return (annualized): -0.0702
Market regime: sideways

Compute portfolio weights (w_DOT-USD, w_IWM) 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_IWM=X.XXXX

Answer: w_DOT-USD=0.0464, w_IWM=0.9536

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000198 - 0.000052) / (0.001490 + 0.000198 - 0.000104)
  Unconstrained: w_DOT-USD=0.0922
  After long-only clamp: w_DOT-USD=0.0922, w_IWM=0.9078.


Question:
Assets: VTI, SCHH
VTI: annualized_mean_return=-0.1512, daily_std=0.0084
SCHH: annualized_mean_return=-0.3024, daily_std=0.0122
Minimum required portfolio return (annualized): -0.2353
Market regime: sideways

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

Answer: w_VTI=1.0000, w_SCHH=0.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000150 - 0.000075) / (0.000071 + 0.000150 - 0.000151)
  Unconstrained: w_VTI=1.0655
  After long-only clamp: w_VTI=1.0000, w_SCHH=0.0000.


AVAX-USD σ=0.0593, CSHI σ=0.0005, ρ=-0.058. Min-variance weights: AVAX-USD=0.001, CSHI=0.999.

Question:
Assets: AVAX-USD, CSHI
AVAX-USD: annualized_mean_return=6.6024, daily_std=0.0593
CSHI: annualized_mean_return=0.0504, daily_std=0.0005
Minimum required portfolio return (annualized): 0.0526
Market regime: sideways

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

Answer: w_AVAX-USD=0.0006, w_CSHI=0.9994

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000002) / (0.003519 + 0.000000 - -0.000004)
  Unconstrained: w_AVAX-USD=0.0006
  After long-only clamp: w_AVAX-USD=0.0006, w_CSHI=0.9994.


Question:
Assets: DOT-USD, DBB
DOT-USD: annualized_mean_return=-0.4788, daily_std=0.0343
DBB: annualized_mean_return=-0.1764, daily_std=0.0113
Minimum required portfolio return (annualized): -0.1840
Market regime: sideways

Compute portfolio weights (w_DOT-USD, w_DBB) 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_DBB=X.XXXX

Answer: w_DOT-USD=0.0251, w_DBB=0.9749

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000129 - 0.000064) / (0.001175 + 0.000129 - 0.000128)
  Unconstrained: w_DOT-USD=0.0550
  After long-only clamp: w_DOT-USD=0.0550, w_DBB=0.9450.


Question:
Assets: IWM, SGOV
IWM: annualized_mean_return=0.7560, daily_std=0.0134
SGOV: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0504
Market regime: sideways

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=0.0001, w_SGOV=0.9999

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000181 + 0.000000 - -0.000001)
  Unconstrained: w_IWM=0.0021
  After long-only clamp: w_IWM=0.0021, w_SGOV=0.9979.


Question:
Assets: BNB-USD, SHY
BNB-USD: annualized_mean_return=1.1844, daily_std=0.0274
SHY: annualized_mean_return=0.0756, daily_std=0.0012
Minimum required portfolio return (annualized): 0.0771
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_SHY) 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_SHY=X.XXXX

Answer: w_BNB-USD=0.0020, w_SHY=0.9980

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - -0.000000) / (0.000752 + 0.000001 - -0.000000)
  Unconstrained: w_BNB-USD=0.0021
  After long-only clamp: w_BNB-USD=0.0021, w_SHY=0.9979.


Question:
Assets: MTUM, WEAT
MTUM: annualized_mean_return=0.4788, daily_std=0.0103
WEAT: annualized_mean_return=-0.6048, daily_std=0.0168
Minimum required portfolio return (annualized): 0.0302
Market regime: sideways

Compute portfolio weights (w_MTUM, w_WEAT) 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_WEAT=X.XXXX

Answer: w_MTUM=0.6972, w_WEAT=0.3028

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000284 - -0.000031) / (0.000106 + 0.000284 - -0.000063)
  Unconstrained: w_MTUM=0.6968
  After long-only clamp: w_MTUM=0.6968, w_WEAT=0.3032.


Question:
Assets: VLUE, SCHH
VLUE: annualized_mean_return=0.0000, daily_std=0.0089
SCHH: annualized_mean_return=-0.0504, daily_std=0.0134
Minimum required portfolio return (annualized): -0.0034
Market regime: sideways

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

Answer: w_VLUE=1.0000, w_SCHH=0.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000180 - 0.000100) / (0.000079 + 0.000180 - 0.000200)
  Unconstrained: w_VLUE=1.3524
  After long-only clamp: w_VLUE=1.0000, w_SCHH=0.0000.


DOT-USD σ=0.0279, VNQI σ=0.0098, ρ=0.078. Min-variance weights: DOT-USD=0.091, VNQI=0.909.

Question:
Assets: DOT-USD, VNQI
DOT-USD: annualized_mean_return=0.0756, daily_std=0.0279
VNQI: annualized_mean_return=0.0504, daily_std=0.0098
Minimum required portfolio return (annualized): 0.0526
Market regime: sideways

Compute portfolio weights (w_DOT-USD, w_VNQI) 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_VNQI=X.XXXX

Answer: w_DOT-USD=0.0911, w_VNQI=0.9089

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000097 - 0.000021) / (0.000778 + 0.000097 - 0.000043)
  Unconstrained: w_DOT-USD=0.0908
  After long-only clamp: w_DOT-USD=0.0908, w_VNQI=0.9092.


Question:
Assets: VEA, LQD
VEA: annualized_mean_return=0.1512, daily_std=0.0090
LQD: annualized_mean_return=-0.0000, daily_std=0.0056
Minimum required portfolio return (annualized): 0.0835
Market regime: sideways

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

Answer: w_VEA=0.5522, w_LQD=0.4478

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000032 - 0.000003) / (0.000080 + 0.000032 - 0.000007)
  Unconstrained: w_VEA=0.2683
  After long-only clamp: w_VEA=0.2683, w_LQD=0.7317.


Question:
Assets: XLRE, SOYB
XLRE: annualized_mean_return=0.1008, daily_std=0.0135
SOYB: annualized_mean_return=-0.2520, daily_std=0.0099
Minimum required portfolio return (annualized): 0.0227
Market regime: sideways

Compute portfolio weights (w_XLRE, w_SOYB) 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_SOYB=X.XXXX

Answer: w_XLRE=0.7786, w_SOYB=0.2214

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000097 - 0.000031) / (0.000183 + 0.000097 - 0.000061)
  Unconstrained: w_XLRE=0.3033
  After long-only clamp: w_XLRE=0.3033, w_SOYB=0.6967.


Question:
Assets: XLRE, DBB
XLRE: annualized_mean_return=-0.2520, daily_std=0.0141
DBB: annualized_mean_return=-0.4032, daily_std=0.0119
Minimum required portfolio return (annualized): -0.3140
Market regime: sideways

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

Answer: w_XLRE=0.5899, w_DBB=0.4101

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000140 - -0.000010) / (0.000197 + 0.000140 - -0.000020)
  Unconstrained: w_XLRE=0.4205
  After long-only clamp: w_XLRE=0.4205, w_DBB=0.5795.


ADA-USD σ=0.0344, BNDX σ=0.0039, ρ=0.055. Min-variance weights: ADA-USD=0.007, BNDX=0.993.

Question:
Assets: ADA-USD, BNDX
ADA-USD: annualized_mean_return=-0.1512, daily_std=0.0344
BNDX: annualized_mean_return=0.1008, daily_std=0.0039
Minimum required portfolio return (annualized): 0.0428
Market regime: sideways

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

Answer: w_ADA-USD=0.0072, w_BNDX=0.9928

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000015 - 0.000007) / (0.001184 + 0.000015 - 0.000015)
  Unconstrained: w_ADA-USD=0.0068
  After long-only clamp: w_ADA-USD=0.0068, w_BNDX=0.9932.


Question:
Assets: SOL-USD, EWJ
SOL-USD: annualized_mean_return=-0.1512, daily_std=0.0351
EWJ: annualized_mean_return=0.4284, daily_std=0.0096
Minimum required portfolio return (annualized): 0.4257
Market regime: sideways

Compute portfolio weights (w_SOL-USD, w_EWJ) 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_EWJ=X.XXXX

Answer: w_SOL-USD=0.0047, w_EWJ=0.9953

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000091 - 0.000083) / (0.001229 + 0.000091 - 0.000165)
  Unconstrained: w_SOL-USD=0.0075
  After long-only clamp: w_SOL-USD=0.0075, w_EWJ=0.9925.


Question:
Assets: XLRE, PDBC
XLRE: annualized_mean_return=0.6048, daily_std=0.0087
PDBC: annualized_mean_return=-0.3276, daily_std=0.0086
Minimum required portfolio return (annualized): 0.3929
Market regime: sideways

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

Answer: w_XLRE=0.7727, w_PDBC=0.2273

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000074 - 0.000002) / (0.000075 + 0.000074 - 0.000004)
  Unconstrained: w_XLRE=0.4986
  After long-only clamp: w_XLRE=0.4986, w_PDBC=0.5014.


Question:
Assets: EFA, CSHI
EFA: annualized_mean_return=0.1260, daily_std=0.0088
CSHI: annualized_mean_return=0.0756, daily_std=0.0008
Minimum required portfolio return (annualized): 0.0943
Market regime: sideways

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

Answer: w_EFA=0.3710, w_CSHI=0.6290

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - 0.000001) / (0.000078 + 0.000001 - 0.000001)
  Unconstrained: w_EFA=0.0012
  After long-only clamp: w_EFA=0.0012, w_CSHI=0.9988.


Question:
Assets: XRP-USD, DBC
XRP-USD: annualized_mean_return=-0.3276, daily_std=0.0534
DBC: annualized_mean_return=0.4032, daily_std=0.0084
Minimum required portfolio return (annualized): 0.3945
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_DBC) 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_DBC=X.XXXX

Answer: w_XRP-USD=0.0119, w_DBC=0.9881

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000071 - 0.000027) / (0.002848 + 0.000071 - 0.000053)
  Unconstrained: w_XRP-USD=0.0155
  After long-only clamp: w_XRP-USD=0.0155, w_DBC=0.9845.


MATIC-USD σ=0.0396, IAU σ=0.0086, ρ=-0.044. Min-variance weights: MATIC-USD=0.053, IAU=0.947.

Question:
Assets: MATIC-USD, IAU
MATIC-USD: annualized_mean_return=2.3184, daily_std=0.0396
IAU: annualized_mean_return=0.0252, daily_std=0.0086
Minimum required portfolio return (annualized): 1.2637
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_IAU) 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_IAU=X.XXXX

Answer: w_MATIC-USD=0.5401, w_IAU=0.4599

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000073 - -0.000015) / (0.001567 + 0.000073 - -0.000030)
  Unconstrained: w_MATIC-USD=0.0529
  After long-only clamp: w_MATIC-USD=0.0529, w_IAU=0.9471.


MATIC-USD σ=0.0399, IYR σ=0.0133, ρ=0.100. Min-variance weights: MATIC-USD=0.074, IYR=0.926.

Question:
Assets: MATIC-USD, IYR
MATIC-USD: annualized_mean_return=2.5200, daily_std=0.0399
IYR: annualized_mean_return=0.1008, daily_std=0.0133
Minimum required portfolio return (annualized): 0.2641
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_IYR) 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_IYR=X.XXXX

Answer: w_MATIC-USD=0.0742, w_IYR=0.9258

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000176 - 0.000053) / (0.001589 + 0.000176 - 0.000106)
  Unconstrained: w_MATIC-USD=0.0741
  After long-only clamp: w_MATIC-USD=0.0741, w_IYR=0.9259.


Question:
Assets: EWJ, SCHP
EWJ: annualized_mean_return=0.1260, daily_std=0.0118
SCHP: annualized_mean_return=-0.0252, daily_std=0.0028
Minimum required portfolio return (annualized): -0.0190
Market regime: sideways

Compute portfolio weights (w_EWJ, w_SCHP) 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_SCHP=X.XXXX

Answer: w_EWJ=0.0523, w_SCHP=0.9477

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000008 - -0.000000) / (0.000139 + 0.000008 - -0.000001)
  Unconstrained: w_EWJ=0.0546
  After long-only clamp: w_EWJ=0.0546, w_SCHP=0.9454.


XLF σ=0.0089, MATIC-USD σ=0.0377, ρ=-0.086. Min-variance weights: XLF=0.931, MATIC-USD=0.069.

Question:
Assets: XLF, MATIC-USD
XLF: annualized_mean_return=0.1512, daily_std=0.0089
MATIC-USD: annualized_mean_return=2.6460, daily_std=0.0377
Minimum required portfolio return (annualized): 0.3071
Market regime: sideways

Compute portfolio weights (w_XLF, w_MATIC-USD) 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_MATIC-USD=X.XXXX

Answer: w_XLF=0.9306, w_MATIC-USD=0.0694

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.001420 - -0.000029) / (0.000079 + 0.001420 - -0.000058)
  Unconstrained: w_XLF=0.9306
  After long-only clamp: w_XLF=0.9306, w_MATIC-USD=0.0694.