Question:
Assets: BTC-USD, BIL
BTC-USD: annualized_mean_return=0.0252, daily_std=0.0262
BIL: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0394
Market regime: sideways

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

Answer: w_BTC-USD=0.0000, w_BIL=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.000684 + 0.000000 - 0.000001)
  Unconstrained: w_BTC-USD=-0.0009
  After long-only clamp: w_BTC-USD=0.0000, w_BIL=1.0000.


Question:
Assets: DOT-USD, PALL
DOT-USD: annualized_mean_return=1.0584, daily_std=0.0515
PALL: annualized_mean_return=-0.6804, daily_std=0.0243
Minimum required portfolio return (annualized): 0.7411
Market regime: sideways

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

Answer: w_DOT-USD=0.8175, w_PALL=0.1825

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000592 - -0.000083) / (0.002653 + 0.000592 - -0.000166)
  Unconstrained: w_DOT-USD=0.1978
  After long-only clamp: w_DOT-USD=0.1978, w_PALL=0.8022.


MATIC-USD σ=0.0615, GLD σ=0.0097, ρ=-0.069. Min-variance weights: MATIC-USD=0.034, GLD=0.966.

Question:
Assets: MATIC-USD, GLD
MATIC-USD: annualized_mean_return=2.5704, daily_std=0.0615
GLD: annualized_mean_return=0.0252, daily_std=0.0097
Minimum required portfolio return (annualized): 0.0678
Market regime: sideways

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

Answer: w_MATIC-USD=0.0342, w_GLD=0.9658

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000094 - -0.000041) / (0.003776 + 0.000094 - -0.000082)
  Unconstrained: w_MATIC-USD=0.0342
  After long-only clamp: w_MATIC-USD=0.0342, w_GLD=0.9658.


LINK-USD σ=0.0273, SOYB σ=0.0130, ρ=-0.148. Min-variance weights: LINK-USD=0.217, SOYB=0.783.

Question:
Assets: LINK-USD, SOYB
LINK-USD: annualized_mean_return=-0.6300, daily_std=0.0273
SOYB: annualized_mean_return=0.4032, daily_std=0.0130
Minimum required portfolio return (annualized): 0.3449
Market regime: sideways

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

Answer: w_LINK-USD=0.0564, w_SOYB=0.9436

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000168 - -0.000052) / (0.000745 + 0.000168 - -0.000105)
  Unconstrained: w_LINK-USD=0.2170
  After long-only clamp: w_LINK-USD=0.2170, w_SOYB=0.7830.


Question:
Assets: XLP, INDS
XLP: annualized_mean_return=0.2268, daily_std=0.0063
INDS: annualized_mean_return=-0.0504, daily_std=0.0120
Minimum required portfolio return (annualized): 0.0893
Market regime: sideways

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

Answer: w_XLP=1.0000, w_INDS=0.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000145 - 0.000049) / (0.000040 + 0.000145 - 0.000098)
  Unconstrained: w_XLP=1.1113
  After long-only clamp: w_XLP=1.0000, w_INDS=0.0000.


Question:
Assets: XLU, ADA-USD
XLU: annualized_mean_return=-0.0000, daily_std=0.0116
ADA-USD: annualized_mean_return=0.8064, daily_std=0.0345
Minimum required portfolio return (annualized): 0.0198
Market regime: sideways

Compute portfolio weights (w_XLU, w_ADA-USD) 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_ADA-USD=X.XXXX

Answer: w_XLU=0.9502, w_ADA-USD=0.0498

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.001191 - 0.000077) / (0.000135 + 0.001191 - 0.000154)
  Unconstrained: w_XLU=0.9504
  After long-only clamp: w_XLU=0.9504, w_ADA-USD=0.0496.


Question:
Assets: FXI, ADA-USD
FXI: annualized_mean_return=0.4536, daily_std=0.0140
ADA-USD: annualized_mean_return=-1.0836, daily_std=0.0251
Minimum required portfolio return (annualized): -0.2179
Market regime: bull

Compute portfolio weights (w_FXI, w_ADA-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_ADA-USD=X.XXXX

Answer: w_FXI=0.7416, w_ADA-USD=0.2584

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000632 - -0.000038) / (0.000195 + 0.000632 - -0.000076)
  Unconstrained: w_FXI=0.7417
  After long-only clamp: w_FXI=0.7417, w_ADA-USD=0.2583.


Question:
Assets: ACWI, INDS
ACWI: annualized_mean_return=0.1260, daily_std=0.0071
INDS: annualized_mean_return=-0.2772, daily_std=0.0112
Minimum required portfolio return (annualized): 0.0725
Market regime: sideways

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

Answer: w_ACWI=1.0000, w_INDS=0.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000125 - 0.000053) / (0.000051 + 0.000125 - 0.000105)
  Unconstrained: w_ACWI=1.0206
  After long-only clamp: w_ACWI=1.0000, w_INDS=0.0000.


Question:
Assets: DOT-USD, JNK
DOT-USD: annualized_mean_return=-0.1512, daily_std=0.0397
JNK: annualized_mean_return=0.0252, daily_std=0.0059
Minimum required portfolio return (annualized): -0.0622
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=0.0427, w_JNK=0.9573

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000035 - -0.000037) / (0.001572 + 0.000035 - -0.000075)
  Unconstrained: w_DOT-USD=0.0429
  After long-only clamp: w_DOT-USD=0.0429, w_JNK=0.9571.


Question:
Assets: DOT-USD, XLK
DOT-USD: annualized_mean_return=-0.8568, daily_std=0.0205
XLK: annualized_mean_return=0.0504, daily_std=0.0108
Minimum required portfolio return (annualized): -0.3861
Market regime: sideways

Compute portfolio weights (w_DOT-USD, w_XLK) 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_XLK=X.XXXX

Answer: w_DOT-USD=0.1299, w_XLK=0.8701

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000116 - 0.000062) / (0.000422 + 0.000116 - 0.000124)
  Unconstrained: w_DOT-USD=0.1297
  After long-only clamp: w_DOT-USD=0.1297, w_XLK=0.8703.


Question:
Assets: ETH-USD, SCHH
ETH-USD: annualized_mean_return=1.6380, daily_std=0.0358
SCHH: annualized_mean_return=-0.1764, daily_std=0.0112
Minimum required portfolio return (annualized): 1.0002
Market regime: sideways

Compute portfolio weights (w_ETH-USD, w_SCHH) 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_SCHH=X.XXXX

Answer: w_ETH-USD=0.6485, w_SCHH=0.3515

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000125 - -0.000041) / (0.001285 + 0.000125 - -0.000081)
  Unconstrained: w_ETH-USD=0.1110
  After long-only clamp: w_ETH-USD=0.1110, w_SCHH=0.8890.


Question:
Assets: DOT-USD, XHB
DOT-USD: annualized_mean_return=0.5544, daily_std=0.0244
XHB: annualized_mean_return=-0.2772, daily_std=0.0158
Minimum required portfolio return (annualized): -0.1398
Market regime: sideways

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

Answer: w_DOT-USD=0.2783, w_XHB=0.7217

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000250 - 0.000034) / (0.000594 + 0.000250 - 0.000067)
  Unconstrained: w_DOT-USD=0.2786
  After long-only clamp: w_DOT-USD=0.2786, w_XHB=0.7214.


Question:
Assets: SOL-USD, SHY
SOL-USD: annualized_mean_return=0.0504, daily_std=0.0396
SHY: annualized_mean_return=0.0504, daily_std=0.0010
Minimum required portfolio return (annualized): 0.0504
Market regime: bull

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

Answer: w_SOL-USD=0.0000, w_SHY=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - 0.000010) / (0.001568 + 0.000001 - 0.000019)
  Unconstrained: w_SOL-USD=-0.0055
  After long-only clamp: w_SOL-USD=0.0000, w_SHY=1.0000.


Question:
Assets: ACWI, XHB
ACWI: annualized_mean_return=-0.2520, daily_std=0.0076
XHB: annualized_mean_return=-0.5292, daily_std=0.0151
Minimum required portfolio return (annualized): -0.3245
Market regime: sideways

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

Answer: w_ACWI=1.0000, w_XHB=0.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000229 - 0.000089) / (0.000058 + 0.000229 - 0.000178)
  Unconstrained: w_ACWI=1.2828
  After long-only clamp: w_ACWI=1.0000, w_XHB=0.0000.


Question:
Assets: AVAX-USD, BNO
AVAX-USD: annualized_mean_return=1.6632, daily_std=0.0467
BNO: annualized_mean_return=-0.2520, daily_std=0.0228
Minimum required portfolio return (annualized): 1.2517
Market regime: sideways

Compute portfolio weights (w_AVAX-USD, w_BNO) 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_BNO=X.XXXX

Answer: w_AVAX-USD=0.7851, w_BNO=0.2149

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000519 - -0.000029) / (0.002182 + 0.000519 - -0.000058)
  Unconstrained: w_AVAX-USD=0.1986
  After long-only clamp: w_AVAX-USD=0.1986, w_BNO=0.8014.


Question:
Assets: MTUM, BNDX
MTUM: annualized_mean_return=-0.0000, daily_std=0.0092
BNDX: annualized_mean_return=0.0504, daily_std=0.0037
Minimum required portfolio return (annualized): 0.0407
Market regime: sideways

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

Answer: w_MTUM=0.1360, w_BNDX=0.8640

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000013 - 0.000000) / (0.000085 + 0.000013 - 0.000000)
  Unconstrained: w_MTUM=0.1354
  After long-only clamp: w_MTUM=0.1354, w_BNDX=0.8646.


MATIC-USD σ=0.0345, BIL σ=0.0002, ρ=0.155. Min-variance weights: MATIC-USD=0.000, BIL=1.000.

Question:
Assets: MATIC-USD, BIL
MATIC-USD: annualized_mean_return=1.1088, daily_std=0.0345
BIL: annualized_mean_return=0.0252, daily_std=0.0002
Minimum required portfolio return (annualized): 0.6258
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=0.5543, w_BIL=0.4457

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.001190 + 0.000000 - 0.000002)
  Unconstrained: w_MATIC-USD=-0.0009
  After long-only clamp: w_MATIC-USD=0.0000, w_BIL=1.0000.


Question:
Assets: QUAL, BIL
QUAL: annualized_mean_return=0.4032, daily_std=0.0073
BIL: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0505
Market regime: sideways

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

Answer: w_QUAL=0.0003, w_BIL=0.9997

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000053 + 0.000000 - 0.000000)
  Unconstrained: w_QUAL=-0.0009
  After long-only clamp: w_QUAL=0.0000, w_BIL=1.0000.


Question:
Assets: XLV, EMB
XLV: annualized_mean_return=-0.3024, daily_std=0.0064
EMB: annualized_mean_return=-0.2268, daily_std=0.0054
Minimum required portfolio return (annualized): -0.2435
Market regime: sideways

Compute portfolio weights (w_XLV, w_EMB) 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_EMB=X.XXXX

Answer: w_XLV=0.2209, w_EMB=0.7791

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000029 - 0.000005) / (0.000041 + 0.000029 - 0.000010)
  Unconstrained: w_XLV=0.4065
  After long-only clamp: w_XLV=0.4065, w_EMB=0.5935.


Question:
Assets: VLUE, ICSH
VLUE: annualized_mean_return=0.3528, daily_std=0.0079
ICSH: annualized_mean_return=0.0504, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0507
Market regime: bull

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

Answer: w_VLUE=0.0012, w_ICSH=0.9988

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000062 + 0.000000 - -0.000000)
  Unconstrained: w_VLUE=0.0046
  After long-only clamp: w_VLUE=0.0046, w_ICSH=0.9954.


Question:
Assets: BTC-USD, LQD
BTC-USD: annualized_mean_return=1.2600, daily_std=0.0191
LQD: annualized_mean_return=-0.1260, daily_std=0.0062
Minimum required portfolio return (annualized): 0.0224
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_LQD) 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_LQD=X.XXXX

Answer: w_BTC-USD=0.1343, w_LQD=0.8657

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000038 - -0.000022) / (0.000365 + 0.000038 - -0.000044)
  Unconstrained: w_BTC-USD=0.1343
  After long-only clamp: w_BTC-USD=0.1343, w_LQD=0.8657.


Question:
Assets: SPY, STIP
SPY: annualized_mean_return=0.1764, daily_std=0.0067
STIP: annualized_mean_return=0.0504, daily_std=0.0012
Minimum required portfolio return (annualized): 0.0509
Market regime: sideways

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

Answer: w_SPY=0.0079, w_STIP=0.9921

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - 0.000001) / (0.000045 + 0.000001 - 0.000001)
  Unconstrained: w_SPY=0.0135
  After long-only clamp: w_SPY=0.0135, w_STIP=0.9865.


Question:
Assets: QUAL, SCHH
QUAL: annualized_mean_return=0.1008, daily_std=0.0084
SCHH: annualized_mean_return=0.0252, daily_std=0.0132
Minimum required portfolio return (annualized): 0.0854
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=1.0000, w_SCHH=0.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000174 - 0.000075) / (0.000071 + 0.000174 - 0.000150)
  Unconstrained: w_QUAL=1.0394
  After long-only clamp: w_QUAL=1.0000, w_SCHH=0.0000.


Question:
Assets: EEM, CSHI
EEM: annualized_mean_return=-0.0252, daily_std=0.0091
CSHI: annualized_mean_return=0.0504, daily_std=0.0005
Minimum required portfolio return (annualized): 0.0064
Market regime: sideways

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

Answer: w_EEM=0.0000, w_CSHI=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.000082 + 0.000000 - 0.000001)
  Unconstrained: w_EEM=-0.0033
  After long-only clamp: w_EEM=0.0000, w_CSHI=1.0000.


Question:
Assets: XLRE, ITB
XLRE: annualized_mean_return=-0.0504, daily_std=0.0135
ITB: annualized_mean_return=0.1260, daily_std=0.0180
Minimum required portfolio return (annualized): 0.0889
Market regime: sideways

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

Answer: w_XLRE=0.2103, w_ITB=0.7897

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000324 - 0.000184) / (0.000183 + 0.000324 - 0.000368)
  Unconstrained: w_XLRE=1.0096
  After long-only clamp: w_XLRE=1.0000, w_ITB=0.0000.


Question:
Assets: XLK, CSHI
XLK: annualized_mean_return=0.3276, daily_std=0.0143
CSHI: annualized_mean_return=0.0504, daily_std=0.0004
Minimum required portfolio return (annualized): 0.0516
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=0.0103, w_CSHI=0.9897

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000002) / (0.000205 + 0.000000 - -0.000003)
  Unconstrained: w_XLK=0.0087
  After long-only clamp: w_XLK=0.0087, w_CSHI=0.9913.


Question:
Assets: XLB, ICSH
XLB: annualized_mean_return=0.4032, daily_std=0.0085
ICSH: annualized_mean_return=0.0504, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0508
Market regime: sideways

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

Answer: w_XLB=0.0014, w_ICSH=0.9986

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000073 + 0.000000 - -0.000000)
  Unconstrained: w_XLB=0.0038
  After long-only clamp: w_XLB=0.0038, w_ICSH=0.9962.


Question:
Assets: VTI, SGOV
VTI: annualized_mean_return=-0.0756, daily_std=0.0109
SGOV: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0329
Market regime: sideways

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

Answer: w_VTI=0.0002, w_SGOV=0.9998

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000119 + 0.000000 - 0.000000)
  Unconstrained: w_VTI=-0.0009
  After long-only clamp: w_VTI=0.0000, w_SGOV=1.0000.


LINK-USD σ=0.0333, REZ σ=0.0093, ρ=0.016. Min-variance weights: LINK-USD=0.068, REZ=0.932.

Question:
Assets: LINK-USD, REZ
LINK-USD: annualized_mean_return=0.5796, daily_std=0.0333
REZ: annualized_mean_return=0.3528, daily_std=0.0093
Minimum required portfolio return (annualized): 0.3601
Market regime: sideways

Compute portfolio weights (w_LINK-USD, w_REZ) 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_REZ=X.XXXX

Answer: w_LINK-USD=0.0682, w_REZ=0.9318

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000086 - 0.000005) / (0.001109 + 0.000086 - 0.000010)
  Unconstrained: w_LINK-USD=0.0682
  After long-only clamp: w_LINK-USD=0.0682, w_REZ=0.9318.


XRP-USD σ=0.0182, ICSH σ=0.0002, ρ=0.173. Min-variance weights: XRP-USD=0.000, ICSH=1.000.

Question:
Assets: XRP-USD, ICSH
XRP-USD: annualized_mean_return=-0.3024, daily_std=0.0182
ICSH: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): -0.1168
Market regime: sideways

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

Answer: w_XRP-USD=0.0000, w_ICSH=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.000332 + 0.000000 - 0.000001)
  Unconstrained: w_XRP-USD=-0.0020
  After long-only clamp: w_XRP-USD=0.0000, w_ICSH=1.0000.


Question:
Assets: EFA, TIP
EFA: annualized_mean_return=0.3276, daily_std=0.0071
TIP: annualized_mean_return=0.0504, daily_std=0.0013
Minimum required portfolio return (annualized): 0.0552
Market regime: sideways

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

Answer: w_EFA=0.0333, w_TIP=0.9667

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000002 - -0.000000) / (0.000051 + 0.000002 - -0.000001)
  Unconstrained: w_EFA=0.0402
  After long-only clamp: w_EFA=0.0402, w_TIP=0.9598.


Question:
Assets: XLP, UNG
XLP: annualized_mean_return=0.1260, daily_std=0.0065
UNG: annualized_mean_return=-0.7308, daily_std=0.0404
Minimum required portfolio return (annualized): -0.2148
Market regime: sideways

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

Answer: w_XLP=1.0000, w_UNG=0.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.001633 - 0.000060) / (0.000042 + 0.001633 - 0.000120)
  Unconstrained: w_XLP=1.0116
  After long-only clamp: w_XLP=1.0000, w_UNG=0.0000.


Question:
Assets: FXI, MORT
FXI: annualized_mean_return=0.1260, daily_std=0.0180
MORT: annualized_mean_return=0.6552, daily_std=0.0155
Minimum required portfolio return (annualized): 0.2642
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=0.3702, w_MORT=0.6298

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000241 - 0.000126) / (0.000322 + 0.000241 - 0.000251)
  Unconstrained: w_FXI=0.3706
  After long-only clamp: w_FXI=0.3706, w_MORT=0.6294.


Question:
Assets: XLK, ICSH
XLK: annualized_mean_return=0.5544, daily_std=0.0117
ICSH: annualized_mean_return=0.0252, daily_std=0.0005
Minimum required portfolio return (annualized): 0.1497
Market regime: sideways

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

Answer: w_XLK=0.2353, w_ICSH=0.7647

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000137 + 0.000000 - 0.000001)
  Unconstrained: w_XLK=-0.0016
  After long-only clamp: w_XLK=0.0000, w_ICSH=1.0000.


Question:
Assets: SOL-USD, ICSH
SOL-USD: annualized_mean_return=0.5040, daily_std=0.0487
ICSH: annualized_mean_return=0.0756, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0761
Market regime: bull

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

Answer: w_SOL-USD=0.0017, w_ICSH=0.9983

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000004) / (0.002376 + 0.000000 - -0.000009)
  Unconstrained: w_SOL-USD=0.0019
  After long-only clamp: w_SOL-USD=0.0019, w_ICSH=0.9981.


Question:
Assets: EEM, VNQ
EEM: annualized_mean_return=0.1764, daily_std=0.0142
VNQ: annualized_mean_return=-0.0756, daily_std=0.0151
Minimum required portfolio return (annualized): 0.1385
Market regime: sideways

Compute portfolio weights (w_EEM, w_VNQ) 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_VNQ=X.XXXX

Answer: w_EEM=0.8496, w_VNQ=0.1504

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000227 - 0.000126) / (0.000201 + 0.000227 - 0.000252)
  Unconstrained: w_EEM=0.5739
  After long-only clamp: w_EEM=0.5739, w_VNQ=0.4261.


Question:
Assets: IVV, BNDX
IVV: annualized_mean_return=0.2772, daily_std=0.0064
BNDX: annualized_mean_return=-0.0252, daily_std=0.0026
Minimum required portfolio return (annualized): 0.0013
Market regime: sideways

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

Answer: w_IVV=0.1528, w_BNDX=0.8472

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000007 - -0.000001) / (0.000042 + 0.000007 - -0.000002)
  Unconstrained: w_IVV=0.1560
  After long-only clamp: w_IVV=0.1560, w_BNDX=0.8440.


AVAX-USD σ=0.0485, VNQ σ=0.0097, ρ=0.253. Min-variance weights: AVAX-USD=0.000, VNQ=1.000.

Question:
Assets: AVAX-USD, VNQ
AVAX-USD: annualized_mean_return=-1.1592, daily_std=0.0485
VNQ: annualized_mean_return=0.3528, daily_std=0.0097
Minimum required portfolio return (annualized): -0.4825
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=0.0000, w_VNQ=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000093 - 0.000119) / (0.002352 + 0.000093 - 0.000237)
  Unconstrained: w_AVAX-USD=-0.0115
  After long-only clamp: w_AVAX-USD=0.0000, w_VNQ=1.0000.


XRP-USD σ=0.0265, CSHI σ=0.0005, ρ=0.136. Min-variance weights: XRP-USD=0.000, CSHI=1.000.

Question:
Assets: XRP-USD, CSHI
XRP-USD: annualized_mean_return=0.8820, daily_std=0.0265
CSHI: annualized_mean_return=0.0504, daily_std=0.0005
Minimum required portfolio return (annualized): 0.2876
Market regime: sideways

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

Answer: w_XRP-USD=0.2852, w_CSHI=0.7148

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000002) / (0.000704 + 0.000000 - 0.000003)
  Unconstrained: w_XRP-USD=-0.0022
  After long-only clamp: w_XRP-USD=0.0000, w_CSHI=1.0000.


Question:
Assets: SOL-USD, REZ
SOL-USD: annualized_mean_return=0.0756, daily_std=0.0574
REZ: annualized_mean_return=0.0504, daily_std=0.0158
Minimum required portfolio return (annualized): 0.0662
Market regime: sideways

Compute portfolio weights (w_SOL-USD, w_REZ) 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_REZ=X.XXXX

Answer: w_SOL-USD=0.6270, w_REZ=0.3730

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000250 - 0.000108) / (0.003298 + 0.000250 - 0.000215)
  Unconstrained: w_SOL-USD=0.0427
  After long-only clamp: w_SOL-USD=0.0427, w_REZ=0.9573.


MATIC-USD σ=0.0461, IYR σ=0.0106, ρ=-0.166. Min-variance weights: MATIC-USD=0.081, IYR=0.919.

Question:
Assets: MATIC-USD, IYR
MATIC-USD: annualized_mean_return=-2.1168, daily_std=0.0461
IYR: annualized_mean_return=0.1008, daily_std=0.0106
Minimum required portfolio return (annualized): -0.5342
Market regime: bull

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=0.0809, w_IYR=0.9191

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000113 - -0.000081) / (0.002126 + 0.000113 - -0.000163)
  Unconstrained: w_MATIC-USD=0.0811
  After long-only clamp: w_MATIC-USD=0.0811, w_IYR=0.9189.


Question:
Assets: XLF, SOL-USD
XLF: annualized_mean_return=0.0504, daily_std=0.0097
SOL-USD: annualized_mean_return=4.1076, daily_std=0.0697
Minimum required portfolio return (annualized): 2.9773
Market regime: sideways

Compute portfolio weights (w_XLF, w_SOL-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_SOL-USD=X.XXXX

Answer: w_XLF=0.2786, w_SOL-USD=0.7214

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.004857 - -0.000052) / (0.000095 + 0.004857 - -0.000104)
  Unconstrained: w_XLF=0.9709
  After long-only clamp: w_XLF=0.9709, w_SOL-USD=0.0291.


Question:
Assets: VLUE, SLV
VLUE: annualized_mean_return=0.5040, daily_std=0.0094
SLV: annualized_mean_return=0.2016, daily_std=0.0155
Minimum required portfolio return (annualized): 0.2965
Market regime: sideways

Compute portfolio weights (w_VLUE, w_SLV) 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_SLV=X.XXXX

Answer: w_VLUE=0.7352, w_SLV=0.2648

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000239 - 0.000004) / (0.000089 + 0.000239 - 0.000009)
  Unconstrained: w_VLUE=0.7358
  After long-only clamp: w_VLUE=0.7358, w_SLV=0.2642.


BNB-USD σ=0.0223, CSHI σ=0.0004, ρ=0.232. Min-variance weights: BNB-USD=0.000, CSHI=1.000.

Question:
Assets: BNB-USD, CSHI
BNB-USD: annualized_mean_return=-0.2268, daily_std=0.0223
CSHI: annualized_mean_return=0.0504, daily_std=0.0004
Minimum required portfolio return (annualized): 0.0057
Market regime: sideways

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

Answer: w_BNB-USD=0.0000, w_CSHI=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000002) / (0.000499 + 0.000000 - 0.000004)
  Unconstrained: w_BNB-USD=-0.0041
  After long-only clamp: w_BNB-USD=0.0000, w_CSHI=1.0000.


Question:
Assets: DOT-USD, FXI
DOT-USD: annualized_mean_return=1.7640, daily_std=0.0404
FXI: annualized_mean_return=0.0504, daily_std=0.0188
Minimum required portfolio return (annualized): 0.1957
Market regime: bull

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

Answer: w_DOT-USD=0.1904, w_FXI=0.8096

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000354 - -0.000039) / (0.001634 + 0.000354 - -0.000077)
  Unconstrained: w_DOT-USD=0.1903
  After long-only clamp: w_DOT-USD=0.1903, w_FXI=0.8097.


Question:
Assets: MTUM, IEF
MTUM: annualized_mean_return=0.5292, daily_std=0.0085
IEF: annualized_mean_return=0.2772, daily_std=0.0057
Minimum required portfolio return (annualized): 0.3168
Market regime: sideways

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

Answer: w_MTUM=0.2849, w_IEF=0.7151

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000033 - 0.000007) / (0.000072 + 0.000033 - 0.000015)
  Unconstrained: w_MTUM=0.2831
  After long-only clamp: w_MTUM=0.2831, w_IEF=0.7169.


DOT-USD σ=0.0237, INDS σ=0.0108, ρ=0.087. Min-variance weights: DOT-USD=0.149, INDS=0.851.

Question:
Assets: DOT-USD, INDS
DOT-USD: annualized_mean_return=0.5040, daily_std=0.0237
INDS: annualized_mean_return=-0.1764, daily_std=0.0108
Minimum required portfolio return (annualized): 0.3311
Market regime: sideways

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

Answer: w_DOT-USD=0.7459, w_INDS=0.2541

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000117 - 0.000022) / (0.000563 + 0.000117 - 0.000044)
  Unconstrained: w_DOT-USD=0.1487
  After long-only clamp: w_DOT-USD=0.1487, w_INDS=0.8513.


ETH-USD σ=0.0368, ICSH σ=0.0003, ρ=0.039. Min-variance weights: ETH-USD=0.000, ICSH=1.000.

Question:
Assets: ETH-USD, ICSH
ETH-USD: annualized_mean_return=1.8396, daily_std=0.0368
ICSH: annualized_mean_return=0.0504, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0504
Market regime: bull

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

Answer: w_ETH-USD=0.0001, w_ICSH=0.9999

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.001353 + 0.000000 - 0.000001)
  Unconstrained: w_ETH-USD=-0.0002
  After long-only clamp: w_ETH-USD=0.0000, w_ICSH=1.0000.


Question:
Assets: XLF, HAUZ
XLF: annualized_mean_return=0.5040, daily_std=0.0068
HAUZ: annualized_mean_return=0.1512, daily_std=0.0105
Minimum required portfolio return (annualized): 0.4952
Market regime: sideways

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

Answer: w_XLF=0.9751, w_HAUZ=0.0249

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000110 - 0.000042) / (0.000047 + 0.000110 - 0.000085)
  Unconstrained: w_XLF=0.9424
  After long-only clamp: w_XLF=0.9424, w_HAUZ=0.0576.


Question:
Assets: USMV, IYR
USMV: annualized_mean_return=0.0756, daily_std=0.0049
IYR: annualized_mean_return=-0.1764, daily_std=0.0110
Minimum required portfolio return (annualized): 0.0556
Market regime: sideways

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

Answer: w_USMV=1.0000, w_IYR=0.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000122 - 0.000040) / (0.000024 + 0.000122 - 0.000080)
  Unconstrained: w_USMV=1.2399
  After long-only clamp: w_USMV=1.0000, w_IYR=0.0000.


Question:
Assets: ETH-USD, DBC
ETH-USD: annualized_mean_return=0.0252, daily_std=0.0376
DBC: annualized_mean_return=0.3528, daily_std=0.0059
Minimum required portfolio return (annualized): 0.2909
Market regime: sideways

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

Answer: w_ETH-USD=0.0000, w_DBC=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000035 - 0.000049) / (0.001414 + 0.000035 - 0.000098)
  Unconstrained: w_ETH-USD=-0.0104
  After long-only clamp: w_ETH-USD=0.0000, w_DBC=1.0000.


MATIC-USD σ=0.0235, ICSH σ=0.0003, ρ=-0.075. Min-variance weights: MATIC-USD=0.001, ICSH=0.999.

Question:
Assets: MATIC-USD, ICSH
MATIC-USD: annualized_mean_return=-1.5372, daily_std=0.0235
ICSH: annualized_mean_return=0.0504, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0503
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) / (0.000552 + 0.000000 - -0.000001)
  Unconstrained: w_MATIC-USD=0.0010
  After long-only clamp: w_MATIC-USD=0.0010, w_ICSH=0.9990.


Question:
Assets: XLE, TLT
XLE: annualized_mean_return=0.5544, daily_std=0.0109
TLT: annualized_mean_return=-0.4284, daily_std=0.0097
Minimum required portfolio return (annualized): -0.0582
Market regime: sideways

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

Answer: w_XLE=0.4310, w_TLT=0.5690

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000094 - 0.000017) / (0.000119 + 0.000094 - 0.000034)
  Unconstrained: w_XLE=0.4311
  After long-only clamp: w_XLE=0.4311, w_TLT=0.5689.


MATIC-USD σ=0.0451, ICSH σ=0.0003, ρ=-0.125. Min-variance weights: MATIC-USD=0.001, ICSH=0.999.

Question:
Assets: MATIC-USD, ICSH
MATIC-USD: annualized_mean_return=-0.2520, daily_std=0.0451
ICSH: annualized_mean_return=0.0756, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0753
Market regime: bull

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=0.0009, w_ICSH=0.9991

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000002) / (0.002038 + 0.000000 - -0.000003)
  Unconstrained: w_MATIC-USD=0.0008
  After long-only clamp: w_MATIC-USD=0.0008, w_ICSH=0.9992.


Question:
Assets: USMV, DBB
USMV: annualized_mean_return=0.2520, daily_std=0.0059
DBB: annualized_mean_return=0.2268, daily_std=0.0126
Minimum required portfolio return (annualized): 0.2497
Market regime: sideways

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

Answer: w_USMV=0.9290, w_DBB=0.0710

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000158 - 0.000025) / (0.000035 + 0.000158 - 0.000050)
  Unconstrained: w_USMV=0.9290
  After long-only clamp: w_USMV=0.9290, w_DBB=0.0710.


Question:
Assets: ADA-USD, TIP
ADA-USD: annualized_mean_return=5.6952, daily_std=0.0576
TIP: annualized_mean_return=0.0252, daily_std=0.0011
Minimum required portfolio return (annualized): 3.9342
Market regime: bull

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

Answer: w_ADA-USD=0.6894, w_TIP=0.3106

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - 0.000015) / (0.003317 + 0.000001 - 0.000030)
  Unconstrained: w_ADA-USD=-0.0042
  After long-only clamp: w_ADA-USD=0.0000, w_TIP=1.0000.


Question:
Assets: ADA-USD, VNQI
ADA-USD: annualized_mean_return=-0.8568, daily_std=0.0342
VNQI: annualized_mean_return=0.5292, daily_std=0.0087
Minimum required portfolio return (annualized): 0.2552
Market regime: sideways

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

Answer: w_ADA-USD=0.0699, w_VNQI=0.9301

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000076 - -0.000013) / (0.001170 + 0.000076 - -0.000026)
  Unconstrained: w_ADA-USD=0.0701
  After long-only clamp: w_ADA-USD=0.0701, w_VNQI=0.9299.


Question:
Assets: FXI, XRP-USD
FXI: annualized_mean_return=1.2852, daily_std=0.0254
XRP-USD: annualized_mean_return=0.4284, daily_std=0.0243
Minimum required portfolio return (annualized): 0.6799
Market regime: sideways

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

Answer: w_FXI=0.4756, w_XRP-USD=0.5244

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000590 - 0.000048) / (0.000645 + 0.000590 - 0.000096)
  Unconstrained: w_FXI=0.4756
  After long-only clamp: w_FXI=0.4756, w_XRP-USD=0.5244.


Question:
Assets: IWM, DBA
IWM: annualized_mean_return=-0.5292, daily_std=0.0098
DBA: annualized_mean_return=-0.1008, daily_std=0.0064
Minimum required portfolio return (annualized): -0.2881
Market regime: sideways

Compute portfolio weights (w_IWM, w_DBA) 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_DBA=X.XXXX

Answer: w_IWM=0.3024, w_DBA=0.6976

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000041 - -0.000002) / (0.000096 + 0.000041 - -0.000003)
  Unconstrained: w_IWM=0.3017
  After long-only clamp: w_IWM=0.3017, w_DBA=0.6983.


Question:
Assets: ADA-USD, DBB
ADA-USD: annualized_mean_return=0.8316, daily_std=0.0370
DBB: annualized_mean_return=-0.3528, daily_std=0.0119
Minimum required portfolio return (annualized): -0.3182
Market regime: sideways

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

Answer: w_ADA-USD=0.0396, w_DBB=0.9604

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000142 - 0.000089) / (0.001372 + 0.000142 - 0.000179)
  Unconstrained: w_ADA-USD=0.0393
  After long-only clamp: w_ADA-USD=0.0393, w_DBB=0.9607.


Question:
Assets: XRP-USD, XLP
XRP-USD: annualized_mean_return=-1.1088, daily_std=0.0473
XLP: annualized_mean_return=0.4536, daily_std=0.0096
Minimum required portfolio return (annualized): -0.3653
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_XLP) 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_XLP=X.XXXX

Answer: w_XRP-USD=0.0892, w_XLP=0.9108

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000091 - -0.000142) / (0.002242 + 0.000091 - -0.000284)
  Unconstrained: w_XRP-USD=0.0892
  After long-only clamp: w_XRP-USD=0.0892, w_XLP=0.9108.


Question:
Assets: XLRE, VCIT
XLRE: annualized_mean_return=-0.3276, daily_std=0.0108
VCIT: annualized_mean_return=-0.1008, daily_std=0.0035
Minimum required portfolio return (annualized): -0.1491
Market regime: sideways

Compute portfolio weights (w_XLRE, w_VCIT) 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_VCIT=X.XXXX

Answer: w_XLRE=0.0360, w_VCIT=0.9640

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000012 - 0.000008) / (0.000116 + 0.000012 - 0.000016)
  Unconstrained: w_XLRE=0.0340
  After long-only clamp: w_XLRE=0.0340, w_VCIT=0.9660.


AVAX-USD σ=0.0415, BNDX σ=0.0026, ρ=-0.082. Min-variance weights: AVAX-USD=0.009, BNDX=0.991.

Question:
Assets: AVAX-USD, BNDX
AVAX-USD: annualized_mean_return=-0.5796, daily_std=0.0415
BNDX: annualized_mean_return=0.0000, daily_std=0.0026
Minimum required portfolio return (annualized): -0.3117
Market regime: sideways

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

Answer: w_AVAX-USD=0.0091, w_BNDX=0.9909

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000007 - -0.000009) / (0.001720 + 0.000007 - -0.000018)
  Unconstrained: w_AVAX-USD=0.0091
  After long-only clamp: w_AVAX-USD=0.0091, w_BNDX=0.9909.


Question:
Assets: XLV, DOT-USD
XLV: annualized_mean_return=0.3024, daily_std=0.0063
DOT-USD: annualized_mean_return=-0.9324, daily_std=0.0347
Minimum required portfolio return (annualized): 0.1858
Market regime: sideways

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

Answer: w_XLV=0.9466, w_DOT-USD=0.0534

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.001204 - -0.000030) / (0.000040 + 0.001204 - -0.000059)
  Unconstrained: w_XLV=0.9470
  After long-only clamp: w_XLV=0.9470, w_DOT-USD=0.0530.


Question:
Assets: DOT-USD, PALL
DOT-USD: annualized_mean_return=-0.0252, daily_std=0.0468
PALL: annualized_mean_return=-1.1592, daily_std=0.0237
Minimum required portfolio return (annualized): -1.0120
Market regime: sideways

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

Answer: w_DOT-USD=0.2337, w_PALL=0.7663

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000562 - -0.000153) / (0.002191 + 0.000562 - -0.000305)
  Unconstrained: w_DOT-USD=0.2336
  After long-only clamp: w_DOT-USD=0.2336, w_PALL=0.7664.


Question:
Assets: ADA-USD, GLD
ADA-USD: annualized_mean_return=0.0504, daily_std=0.0281
GLD: annualized_mean_return=0.5040, daily_std=0.0083
Minimum required portfolio return (annualized): 0.4581
Market regime: sideways

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

Answer: w_ADA-USD=0.0354, w_GLD=0.9646

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000068 - 0.000041) / (0.000789 + 0.000068 - 0.000082)
  Unconstrained: w_ADA-USD=0.0352
  After long-only clamp: w_ADA-USD=0.0352, w_GLD=0.9648.


Question:
Assets: XLP, DBB
XLP: annualized_mean_return=0.2268, daily_std=0.0066
DBB: annualized_mean_return=-0.4284, daily_std=0.0119
Minimum required portfolio return (annualized): 0.1375
Market regime: sideways

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

Answer: w_XLP=0.8637, w_DBB=0.1363

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000141 - -0.000015) / (0.000044 + 0.000141 - -0.000030)
  Unconstrained: w_XLP=0.7260
  After long-only clamp: w_XLP=0.7260, w_DBB=0.2740.


Question:
Assets: XLF, LQD
XLF: annualized_mean_return=0.5544, daily_std=0.0085
LQD: annualized_mean_return=0.4032, daily_std=0.0061
Minimum required portfolio return (annualized): 0.4338
Market regime: sideways

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

Answer: w_XLF=0.2996, w_LQD=0.7004

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000037 - 0.000010) / (0.000073 + 0.000037 - 0.000021)
  Unconstrained: w_XLF=0.2981
  After long-only clamp: w_XLF=0.2981, w_LQD=0.7019.


Question:
Assets: DOT-USD, TLH
DOT-USD: annualized_mean_return=-0.0504, daily_std=0.0250
TLH: annualized_mean_return=-0.1260, daily_std=0.0079
Minimum required portfolio return (annualized): -0.1225
Market regime: sideways

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

Answer: w_DOT-USD=0.0464, w_TLH=0.9536

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000062 - 0.000033) / (0.000625 + 0.000062 - 0.000066)
  Unconstrained: w_DOT-USD=0.0464
  After long-only clamp: w_DOT-USD=0.0464, w_TLH=0.9536.


Question:
Assets: BNB-USD, EWJ
BNB-USD: annualized_mean_return=0.5040, daily_std=0.0229
EWJ: annualized_mean_return=0.0504, daily_std=0.0100
Minimum required portfolio return (annualized): 0.4117
Market regime: sideways

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

Answer: w_BNB-USD=0.7965, w_EWJ=0.2035

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000101 - -0.000092) / (0.000523 + 0.000101 - -0.000185)
  Unconstrained: w_BNB-USD=0.2391
  After long-only clamp: w_BNB-USD=0.2391, w_EWJ=0.7609.


Question:
Assets: XLY, BIL
XLY: annualized_mean_return=0.8064, daily_std=0.0106
BIL: annualized_mean_return=0.0756, daily_std=0.0002
Minimum required portfolio return (annualized): 0.6233
Market regime: bull

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

Answer: w_XLY=0.7495, w_BIL=0.2505

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000113 + 0.000000 - 0.000000)
  Unconstrained: w_XLY=-0.0015
  After long-only clamp: w_XLY=0.0000, w_BIL=1.0000.


BTC-USD σ=0.0174, INDS σ=0.0101, ρ=0.085. Min-variance weights: BTC-USD=0.231, INDS=0.769.

Question:
Assets: BTC-USD, INDS
BTC-USD: annualized_mean_return=-0.5544, daily_std=0.0174
INDS: annualized_mean_return=-0.1008, daily_std=0.0101
Minimum required portfolio return (annualized): -0.2231
Market regime: sideways

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

Answer: w_BTC-USD=0.2308, w_INDS=0.7692

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000101 - 0.000015) / (0.000303 + 0.000101 - 0.000030)
  Unconstrained: w_BTC-USD=0.2309
  After long-only clamp: w_BTC-USD=0.2309, w_INDS=0.7691.


Question:
Assets: SOL-USD, XHB
SOL-USD: annualized_mean_return=2.5956, daily_std=0.0372
XHB: annualized_mean_return=0.0756, daily_std=0.0145
Minimum required portfolio return (annualized): 2.0436
Market regime: sideways

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

Answer: w_SOL-USD=0.7810, w_XHB=0.2190

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000209 - 0.000038) / (0.001387 + 0.000209 - 0.000077)
  Unconstrained: w_SOL-USD=0.1124
  After long-only clamp: w_SOL-USD=0.1124, w_XHB=0.8876.


Question:
Assets: XRP-USD, CSHI
XRP-USD: annualized_mean_return=0.7812, daily_std=0.0340
CSHI: annualized_mean_return=0.0504, daily_std=0.0004
Minimum required portfolio return (annualized): 0.0511
Market regime: sideways

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

Answer: w_XRP-USD=0.0010, w_CSHI=0.9990

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000001) / (0.001155 + 0.000000 - -0.000002)
  Unconstrained: w_XRP-USD=0.0010
  After long-only clamp: w_XRP-USD=0.0010, w_CSHI=0.9990.


Question:
Assets: XLK, BNB-USD
XLK: annualized_mean_return=0.7056, daily_std=0.0116
BNB-USD: annualized_mean_return=-1.3356, daily_std=0.0251
Minimum required portfolio return (annualized): 0.6212
Market regime: sideways

Compute portfolio weights (w_XLK, w_BNB-USD) 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_BNB-USD=X.XXXX

Answer: w_XLK=0.9587, w_BNB-USD=0.0413

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000630 - -0.000017) / (0.000135 + 0.000630 - -0.000034)
  Unconstrained: w_XLK=0.8099
  After long-only clamp: w_XLK=0.8099, w_BNB-USD=0.1901.


Question:
Assets: IVV, CSHI
IVV: annualized_mean_return=0.2016, daily_std=0.0080
CSHI: annualized_mean_return=0.0504, daily_std=0.0005
Minimum required portfolio return (annualized): 0.0509
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=0.0042, w_CSHI=0.9958

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000064 + 0.000000 - -0.000001)
  Unconstrained: w_IVV=0.0096
  After long-only clamp: w_IVV=0.0096, w_CSHI=0.9904.


Question:
Assets: ETH-USD, LQD
ETH-USD: annualized_mean_return=1.9908, daily_std=0.0344
LQD: annualized_mean_return=-0.0000, daily_std=0.0045
Minimum required portfolio return (annualized): 0.8256
Market regime: bull

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

Answer: w_ETH-USD=0.4147, w_LQD=0.5853

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000020 - -0.000012) / (0.001181 + 0.000020 - -0.000023)
  Unconstrained: w_ETH-USD=0.0262
  After long-only clamp: w_ETH-USD=0.0262, w_LQD=0.9738.


Question:
Assets: XLI, BNB-USD
XLI: annualized_mean_return=0.3276, daily_std=0.0096
BNB-USD: annualized_mean_return=-0.9072, daily_std=0.0270
Minimum required portfolio return (annualized): -0.0334
Market regime: sideways

Compute portfolio weights (w_XLI, w_BNB-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_BNB-USD=X.XXXX

Answer: w_XLI=0.8569, w_BNB-USD=0.1431

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000731 - -0.000035) / (0.000093 + 0.000731 - -0.000070)
  Unconstrained: w_XLI=0.8568
  After long-only clamp: w_XLI=0.8568, w_BNB-USD=0.1432.


Question:
Assets: ADA-USD, GLD
ADA-USD: annualized_mean_return=-0.3780, daily_std=0.0431
GLD: annualized_mean_return=0.0000, daily_std=0.0072
Minimum required portfolio return (annualized): -0.1173
Market regime: sideways

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

Answer: w_ADA-USD=0.0400, w_GLD=0.9600

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000052 - -0.000027) / (0.001858 + 0.000052 - -0.000055)
  Unconstrained: w_ADA-USD=0.0403
  After long-only clamp: w_ADA-USD=0.0403, w_GLD=0.9597.


Question:
Assets: VTI, SCHH
VTI: annualized_mean_return=0.3024, daily_std=0.0066
SCHH: annualized_mean_return=0.1260, daily_std=0.0091
Minimum required portfolio return (annualized): 0.2019
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=0.7915, w_SCHH=0.2085

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000084 - 0.000030) / (0.000044 + 0.000084 - 0.000060)
  Unconstrained: w_VTI=0.7928
  After long-only clamp: w_VTI=0.7928, w_SCHH=0.2072.


Question:
Assets: XLV, SOL-USD
XLV: annualized_mean_return=-0.2016, daily_std=0.0059
SOL-USD: annualized_mean_return=1.3860, daily_std=0.0357
Minimum required portfolio return (annualized): -0.1508
Market regime: sideways

Compute portfolio weights (w_XLV, w_SOL-USD) 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_SOL-USD=X.XXXX

Answer: w_XLV=0.9361, w_SOL-USD=0.0639

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.001273 - -0.000056) / (0.000035 + 0.001273 - -0.000113)
  Unconstrained: w_XLV=0.9358
  After long-only clamp: w_XLV=0.9358, w_SOL-USD=0.0642.


LINK-USD σ=0.0423, DBB σ=0.0107, ρ=0.002. Min-variance weights: LINK-USD=0.060, DBB=0.940.

Question:
Assets: LINK-USD, DBB
LINK-USD: annualized_mean_return=-0.0504, daily_std=0.0423
DBB: annualized_mean_return=0.8316, daily_std=0.0107
Minimum required portfolio return (annualized): 0.8183
Market regime: sideways

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

Answer: w_LINK-USD=0.0151, w_DBB=0.9849

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000115 - 0.000001) / (0.001792 + 0.000115 - 0.000002)
  Unconstrained: w_LINK-USD=0.0599
  After long-only clamp: w_LINK-USD=0.0599, w_DBB=0.9401.


Question:
Assets: ACWI, SCHH
ACWI: annualized_mean_return=0.0504, daily_std=0.0094
SCHH: annualized_mean_return=0.6300, daily_std=0.0087
Minimum required portfolio return (annualized): 0.4903
Market regime: sideways

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

Answer: w_ACWI=0.2410, w_SCHH=0.7590

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000076 - 0.000033) / (0.000088 + 0.000076 - 0.000065)
  Unconstrained: w_ACWI=0.4391
  After long-only clamp: w_ACWI=0.4391, w_SCHH=0.5609.


Question:
Assets: ADA-USD, EMB
ADA-USD: annualized_mean_return=-0.4032, daily_std=0.0431
EMB: annualized_mean_return=0.1008, daily_std=0.0049
Minimum required portfolio return (annualized): -0.1357
Market regime: sideways

Compute portfolio weights (w_ADA-USD, w_EMB) 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_EMB=X.XXXX

Answer: w_ADA-USD=0.0158, w_EMB=0.9842

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000024 - -0.000006) / (0.001858 + 0.000024 - -0.000013)
  Unconstrained: w_ADA-USD=0.0160
  After long-only clamp: w_ADA-USD=0.0160, w_EMB=0.9840.


Question:
Assets: XLB, REZ
XLB: annualized_mean_return=-0.1260, daily_std=0.0118
REZ: annualized_mean_return=-0.0252, daily_std=0.0136
Minimum required portfolio return (annualized): -0.0389
Market regime: sideways

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

Answer: w_XLB=0.1359, w_REZ=0.8641

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000185 - 0.000089) / (0.000138 + 0.000185 - 0.000178)
  Unconstrained: w_XLB=0.6592
  After long-only clamp: w_XLB=0.6592, w_REZ=0.3408.


Question:
Assets: MTUM, BIL
MTUM: annualized_mean_return=0.6804, daily_std=0.0096
BIL: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.4408
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=0.6197, w_BIL=0.3803

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000093 + 0.000000 - -0.000000)
  Unconstrained: w_MTUM=0.0005
  After long-only clamp: w_MTUM=0.0005, w_BIL=0.9995.


Question:
Assets: SOL-USD, XHB
SOL-USD: annualized_mean_return=-0.3780, daily_std=0.0385
XHB: annualized_mean_return=0.8568, daily_std=0.0129
Minimum required portfolio return (annualized): 0.8080
Market regime: sideways

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

Answer: w_SOL-USD=0.0395, w_XHB=0.9605

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000166 - 0.000090) / (0.001481 + 0.000166 - 0.000180)
  Unconstrained: w_SOL-USD=0.0519
  After long-only clamp: w_SOL-USD=0.0519, w_XHB=0.9481.


Question:
Assets: VEA, SGOV
VEA: annualized_mean_return=0.7056, daily_std=0.0105
SGOV: annualized_mean_return=0.0252, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0253
Market regime: sideways

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

Answer: w_VEA=0.0002, w_SGOV=0.9998

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000109 + 0.000000 - 0.000001)
  Unconstrained: w_VEA=-0.0035
  After long-only clamp: w_VEA=0.0000, w_SGOV=1.0000.


AVAX-USD σ=0.0450, INDS σ=0.0099, ρ=-0.026. Min-variance weights: AVAX-USD=0.051, INDS=0.949.

Question:
Assets: AVAX-USD, INDS
AVAX-USD: annualized_mean_return=2.0412, daily_std=0.0450
INDS: annualized_mean_return=-0.1764, daily_std=0.0099
Minimum required portfolio return (annualized): 1.0864
Market regime: sideways

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

Answer: w_AVAX-USD=0.5694, w_INDS=0.4306

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000098 - -0.000012) / (0.002023 + 0.000098 - -0.000024)
  Unconstrained: w_AVAX-USD=0.0514
  After long-only clamp: w_AVAX-USD=0.0514, w_INDS=0.9486.


Question:
Assets: ADA-USD, DBA
ADA-USD: annualized_mean_return=0.2772, daily_std=0.0350
DBA: annualized_mean_return=0.1008, daily_std=0.0063
Minimum required portfolio return (annualized): 0.1733
Market regime: sideways

Compute portfolio weights (w_ADA-USD, w_DBA) 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_DBA=X.XXXX

Answer: w_ADA-USD=0.4110, w_DBA=0.5890

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000039 - 0.000012) / (0.001226 + 0.000039 - 0.000023)
  Unconstrained: w_ADA-USD=0.0223
  After long-only clamp: w_ADA-USD=0.0223, w_DBA=0.9777.


Question:
Assets: EFA, CSHI
EFA: annualized_mean_return=0.1512, daily_std=0.0096
CSHI: annualized_mean_return=0.0504, daily_std=0.0012
Minimum required portfolio return (annualized): 0.0822
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=0.3155, w_CSHI=0.6845

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - 0.000000) / (0.000091 + 0.000001 - 0.000000)
  Unconstrained: w_EFA=0.0138
  After long-only clamp: w_EFA=0.0138, w_CSHI=0.9862.


Question:
Assets: ETH-USD, IEF
ETH-USD: annualized_mean_return=0.4284, daily_std=0.0171
IEF: annualized_mean_return=-0.2520, daily_std=0.0050
Minimum required portfolio return (annualized): 0.2420
Market regime: sideways

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=0.7260, w_IEF=0.2740

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000025 - -0.000016) / (0.000293 + 0.000025 - -0.000031)
  Unconstrained: w_ETH-USD=0.1166
  After long-only clamp: w_ETH-USD=0.1166, w_IEF=0.8834.


Question:
Assets: BTC-USD, TLT
BTC-USD: annualized_mean_return=-0.4788, daily_std=0.0173
TLT: annualized_mean_return=-0.5040, daily_std=0.0097
Minimum required portfolio return (annualized): -0.4984
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_TLT) 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_TLT=X.XXXX

Answer: w_BTC-USD=0.2606, w_TLT=0.7394

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000094 - -0.000017) / (0.000299 + 0.000094 - -0.000034)
  Unconstrained: w_BTC-USD=0.2604
  After long-only clamp: w_BTC-USD=0.2604, w_TLT=0.7396.


Question:
Assets: XLK, MORT
XLK: annualized_mean_return=0.1260, daily_std=0.0116
MORT: annualized_mean_return=-0.2268, daily_std=0.0150
Minimum required portfolio return (annualized): 0.0535
Market regime: sideways

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

Answer: w_XLK=0.7945, w_MORT=0.2055

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000225 - 0.000063) / (0.000135 + 0.000225 - 0.000127)
  Unconstrained: w_XLK=0.6939
  After long-only clamp: w_XLK=0.6939, w_MORT=0.3061.


Question:
Assets: SPY, SOYB
SPY: annualized_mean_return=0.3528, daily_std=0.0072
SOYB: annualized_mean_return=-0.0756, daily_std=0.0083
Minimum required portfolio return (annualized): 0.0240
Market regime: sideways

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

Answer: w_SPY=0.5811, w_SOYB=0.4189

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000068 - 0.000012) / (0.000053 + 0.000068 - 0.000024)
  Unconstrained: w_SPY=0.5807
  After long-only clamp: w_SPY=0.5807, w_SOYB=0.4193.


Question:
Assets: XLE, IYR
XLE: annualized_mean_return=-0.0000, daily_std=0.0132
IYR: annualized_mean_return=0.3276, daily_std=0.0086
Minimum required portfolio return (annualized): 0.2911
Market regime: sideways

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

Answer: w_XLE=0.1114, w_IYR=0.8886

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000074 - 0.000015) / (0.000174 + 0.000074 - 0.000029)
  Unconstrained: w_XLE=0.2701
  After long-only clamp: w_XLE=0.2701, w_IYR=0.7299.


Question:
Assets: LINK-USD, UNG
LINK-USD: annualized_mean_return=-0.3780, daily_std=0.0284
UNG: annualized_mean_return=-0.6048, daily_std=0.0401
Minimum required portfolio return (annualized): -0.4846
Market regime: sideways

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

Answer: w_LINK-USD=0.6486, w_UNG=0.3514

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.001609 - -0.000144) / (0.000806 + 0.001609 - -0.000288)
  Unconstrained: w_LINK-USD=0.6485
  After long-only clamp: w_LINK-USD=0.6485, w_UNG=0.3515.


Question:
Assets: XLP, VCIT
XLP: annualized_mean_return=0.2772, daily_std=0.0071
VCIT: annualized_mean_return=0.0756, daily_std=0.0038
Minimum required portfolio return (annualized): 0.2458
Market regime: sideways

Compute portfolio weights (w_XLP, w_VCIT) 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_VCIT=X.XXXX

Answer: w_XLP=0.8442, w_VCIT=0.1558

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000015 - -0.000008) / (0.000051 + 0.000015 - -0.000015)
  Unconstrained: w_XLP=0.2758
  After long-only clamp: w_XLP=0.2758, w_VCIT=0.7242.


Question:
Assets: IVV, SOYB
IVV: annualized_mean_return=0.1260, daily_std=0.0082
SOYB: annualized_mean_return=-0.1512, daily_std=0.0098
Minimum required portfolio return (annualized): 0.0951
Market regime: sideways

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

Answer: w_IVV=0.8885, w_SOYB=0.1115

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000095 - 0.000016) / (0.000067 + 0.000095 - 0.000032)
  Unconstrained: w_IVV=0.6083
  After long-only clamp: w_IVV=0.6083, w_SOYB=0.3917.


Question:
Assets: SOL-USD, PALL
SOL-USD: annualized_mean_return=0.0504, daily_std=0.0404
PALL: annualized_mean_return=-0.2016, daily_std=0.0198
Minimum required portfolio return (annualized): -0.1488
Market regime: sideways

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

Answer: w_SOL-USD=0.2154, w_PALL=0.7846

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000394 - -0.000076) / (0.001635 + 0.000394 - -0.000152)
  Unconstrained: w_SOL-USD=0.2154
  After long-only clamp: w_SOL-USD=0.2154, w_PALL=0.7846.


Question:
Assets: QQQ, BTC-USD
QQQ: annualized_mean_return=-0.0504, daily_std=0.0104
BTC-USD: annualized_mean_return=-0.1008, daily_std=0.0345
Minimum required portfolio return (annualized): -0.0778
Market regime: sideways

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

Answer: w_QQQ=0.9168, w_BTC-USD=0.0832

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.001193 - -0.000001) / (0.000107 + 0.001193 - -0.000002)
  Unconstrained: w_QQQ=0.9167
  After long-only clamp: w_QQQ=0.9167, w_BTC-USD=0.0833.


DOT-USD σ=0.0171, SOYB σ=0.0122, ρ=0.135. Min-variance weights: DOT-USD=0.314, SOYB=0.686.

Question:
Assets: DOT-USD, SOYB
DOT-USD: annualized_mean_return=-1.1088, daily_std=0.0171
SOYB: annualized_mean_return=0.1260, daily_std=0.0122
Minimum required portfolio return (annualized): -0.0453
Market regime: sideways

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

Answer: w_DOT-USD=0.1387, w_SOYB=0.8613

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000149 - 0.000028) / (0.000292 + 0.000149 - 0.000056)
  Unconstrained: w_DOT-USD=0.3142
  After long-only clamp: w_DOT-USD=0.3142, w_SOYB=0.6858.


MATIC-USD σ=0.0323, ICSH σ=0.0003, ρ=0.163. Min-variance weights: MATIC-USD=0.000, ICSH=1.000.

Question:
Assets: MATIC-USD, ICSH
MATIC-USD: annualized_mean_return=0.2520, daily_std=0.0323
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=0.0000, w_ICSH=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000002) / (0.001043 + 0.000000 - 0.000003)
  Unconstrained: w_MATIC-USD=-0.0014
  After long-only clamp: w_MATIC-USD=0.0000, w_ICSH=1.0000.


Question:
Assets: XLF, DBB
XLF: annualized_mean_return=0.4788, daily_std=0.0063
DBB: annualized_mean_return=0.0000, daily_std=0.0083
Minimum required portfolio return (annualized): 0.2458
Market regime: bull

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

Answer: w_XLF=0.6519, w_DBB=0.3481

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000068 - 0.000008) / (0.000040 + 0.000068 - 0.000015)
  Unconstrained: w_XLF=0.6511
  After long-only clamp: w_XLF=0.6511, w_DBB=0.3489.


MATIC-USD σ=0.0398, HAUZ σ=0.0099, ρ=0.104. Min-variance weights: MATIC-USD=0.035, HAUZ=0.965.

Question:
Assets: MATIC-USD, HAUZ
MATIC-USD: annualized_mean_return=2.5704, daily_std=0.0398
HAUZ: annualized_mean_return=0.1764, daily_std=0.0099
Minimum required portfolio return (annualized): 0.8894
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_HAUZ) 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_HAUZ=X.XXXX

Answer: w_MATIC-USD=0.2978, w_HAUZ=0.7022

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000097 - 0.000041) / (0.001586 + 0.000097 - 0.000081)
  Unconstrained: w_MATIC-USD=0.0354
  After long-only clamp: w_MATIC-USD=0.0354, w_HAUZ=0.9646.


Question:
Assets: BTC-USD, BNDX
BTC-USD: annualized_mean_return=-0.8820, daily_std=0.0250
BNDX: annualized_mean_return=0.1008, daily_std=0.0024
Minimum required portfolio return (annualized): 0.0829
Market regime: sideways

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

Answer: w_BTC-USD=0.0170, w_BNDX=0.9830

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000006 - -0.000005) / (0.000625 + 0.000006 - -0.000010)
  Unconstrained: w_BTC-USD=0.0173
  After long-only clamp: w_BTC-USD=0.0173, w_BNDX=0.9827.


Question:
Assets: SOL-USD, HAUZ
SOL-USD: annualized_mean_return=2.6964, daily_std=0.0696
HAUZ: annualized_mean_return=0.3528, daily_std=0.0102
Minimum required portfolio return (annualized): 1.7785
Market regime: sideways

Compute portfolio weights (w_SOL-USD, w_HAUZ) 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_HAUZ=X.XXXX

Answer: w_SOL-USD=0.6083, w_HAUZ=0.3917

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000104 - -0.000030) / (0.004839 + 0.000104 - -0.000061)
  Unconstrained: w_SOL-USD=0.0268
  After long-only clamp: w_SOL-USD=0.0268, w_HAUZ=0.9732.


Question:
Assets: XLY, PALL
XLY: annualized_mean_return=-0.2016, daily_std=0.0115
PALL: annualized_mean_return=-0.0504, daily_std=0.0167
Minimum required portfolio return (annualized): -0.0893
Market regime: sideways

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

Answer: w_XLY=0.2573, w_PALL=0.7427

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000278 - -0.000032) / (0.000133 + 0.000278 - -0.000064)
  Unconstrained: w_XLY=0.6531
  After long-only clamp: w_XLY=0.6531, w_PALL=0.3469.


AVAX-USD σ=0.0651, USO σ=0.0208, ρ=0.018. Min-variance weights: AVAX-USD=0.088, USO=0.912.

Question:
Assets: AVAX-USD, USO
AVAX-USD: annualized_mean_return=5.3676, daily_std=0.0651
USO: annualized_mean_return=-0.5040, daily_std=0.0208
Minimum required portfolio return (annualized): 3.6135
Market regime: sideways

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

Answer: w_AVAX-USD=0.7013, w_USO=0.2987

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000431 - 0.000024) / (0.004243 + 0.000431 - 0.000048)
  Unconstrained: w_AVAX-USD=0.0880
  After long-only clamp: w_AVAX-USD=0.0880, w_USO=0.9120.


Question:
Assets: AVAX-USD, UNG
AVAX-USD: annualized_mean_return=1.2852, daily_std=0.0295
UNG: annualized_mean_return=-0.2772, daily_std=0.0273
Minimum required portfolio return (annualized): 0.3552
Market regime: sideways

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

Answer: w_AVAX-USD=0.4698, w_UNG=0.5302

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000743 - -0.000231) / (0.000868 + 0.000743 - -0.000463)
  Unconstrained: w_AVAX-USD=0.4698
  After long-only clamp: w_AVAX-USD=0.4698, w_UNG=0.5302.


MATIC-USD σ=0.0434, STIP σ=0.0022, ρ=0.186. Min-variance weights: MATIC-USD=0.000, STIP=1.000.

Question:
Assets: MATIC-USD, STIP
MATIC-USD: annualized_mean_return=-0.0252, daily_std=0.0434
STIP: annualized_mean_return=0.0504, daily_std=0.0022
Minimum required portfolio return (annualized): 0.0389
Market regime: sideways

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

Answer: w_MATIC-USD=0.0000, w_STIP=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000005 - 0.000018) / (0.001880 + 0.000005 - 0.000035)
  Unconstrained: w_MATIC-USD=-0.0070
  After long-only clamp: w_MATIC-USD=0.0000, w_STIP=1.0000.


Question:
Assets: FXI, MORT
FXI: annualized_mean_return=-0.6300, daily_std=0.0159
MORT: annualized_mean_return=-0.8820, daily_std=0.0146
Minimum required portfolio return (annualized): -0.7855
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=0.4157, w_MORT=0.5843

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000214 - 0.000117) / (0.000254 + 0.000214 - 0.000233)
  Unconstrained: w_FXI=0.4160
  After long-only clamp: w_FXI=0.4160, w_MORT=0.5840.


BNB-USD σ=0.0254, SCHH σ=0.0139, ρ=0.066. Min-variance weights: BNB-USD=0.213, SCHH=0.786.

Question:
Assets: BNB-USD, SCHH
BNB-USD: annualized_mean_return=0.3780, daily_std=0.0254
SCHH: annualized_mean_return=-0.2520, daily_std=0.0139
Minimum required portfolio return (annualized): 0.0538
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_SCHH) 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_SCHH=X.XXXX

Answer: w_BNB-USD=0.4854, w_SCHH=0.5146

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000193 - 0.000023) / (0.000647 + 0.000193 - 0.000047)
  Unconstrained: w_BNB-USD=0.2135
  After long-only clamp: w_BNB-USD=0.2135, w_SCHH=0.7865.


Question:
Assets: XRP-USD, ICSH
XRP-USD: annualized_mean_return=0.1512, daily_std=0.0261
ICSH: annualized_mean_return=0.0504, daily_std=0.0003
Minimum required portfolio return (annualized): 0.0505
Market regime: sideways

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

Answer: w_XRP-USD=0.0016, w_ICSH=0.9984

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000001) / (0.000679 + 0.000000 - -0.000002)
  Unconstrained: w_XRP-USD=0.0016
  After long-only clamp: w_XRP-USD=0.0016, w_ICSH=0.9984.


Question:
Assets: XLF, SGOV
XLF: annualized_mean_return=-0.2520, daily_std=0.0132
SGOV: annualized_mean_return=0.0504, daily_std=0.0001
Minimum required portfolio return (annualized): -0.0843
Market regime: sideways

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

Answer: w_XLF=0.0001, w_SGOV=0.9999

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000175 + 0.000000 - 0.000000)
  Unconstrained: w_XLF=0.0000
  After long-only clamp: w_XLF=0.0000, w_SGOV=1.0000.


LINK-USD σ=0.0453, IGOV σ=0.0060, ρ=-0.176. Min-variance weights: LINK-USD=0.038, IGOV=0.962.

Question:
Assets: LINK-USD, IGOV
LINK-USD: annualized_mean_return=0.5796, daily_std=0.0453
IGOV: annualized_mean_return=-0.1512, daily_std=0.0060
Minimum required portfolio return (annualized): 0.3599
Market regime: sideways

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

Answer: w_LINK-USD=0.6994, w_IGOV=0.3006

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000036 - -0.000048) / (0.002054 + 0.000036 - -0.000096)
  Unconstrained: w_LINK-USD=0.0384
  After long-only clamp: w_LINK-USD=0.0384, w_IGOV=0.9616.


Question:
Assets: IWM, SCHH
IWM: annualized_mean_return=0.2520, daily_std=0.0107
SCHH: annualized_mean_return=0.1008, daily_std=0.0092
Minimum required portfolio return (annualized): 0.1298
Market regime: sideways

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

Answer: w_IWM=0.2922, w_SCHH=0.7078

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000086 - 0.000065) / (0.000115 + 0.000086 - 0.000130)
  Unconstrained: w_IWM=0.2925
  After long-only clamp: w_IWM=0.2925, w_SCHH=0.7075.


AVAX-USD σ=0.0457, CSHI σ=0.0005, ρ=-0.025. Min-variance weights: AVAX-USD=0.000, CSHI=1.000.

Question:
Assets: AVAX-USD, CSHI
AVAX-USD: annualized_mean_return=1.4616, daily_std=0.0457
CSHI: annualized_mean_return=0.0756, daily_std=0.0005
Minimum required portfolio return (annualized): 0.5781
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=0.3626, w_CSHI=0.6374

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000001) / (0.002086 + 0.000000 - -0.000001)
  Unconstrained: w_AVAX-USD=0.0004
  After long-only clamp: w_AVAX-USD=0.0004, w_CSHI=0.9996.


AVAX-USD σ=0.0513, SCHH σ=0.0133, ρ=0.188. Min-variance weights: AVAX-USD=0.019, SCHH=0.981.

Question:
Assets: AVAX-USD, SCHH
AVAX-USD: annualized_mean_return=4.2336, daily_std=0.0513
SCHH: annualized_mean_return=-0.1008, daily_std=0.0133
Minimum required portfolio return (annualized): 2.2719
Market regime: sideways

Compute portfolio weights (w_AVAX-USD, w_SCHH) 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_SCHH=X.XXXX

Answer: w_AVAX-USD=0.5474, w_SCHH=0.4526

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000176 - 0.000128) / (0.002628 + 0.000176 - 0.000256)
  Unconstrained: w_AVAX-USD=0.0187
  After long-only clamp: w_AVAX-USD=0.0187, w_SCHH=0.9813.


Question:
Assets: ACWI, IGOV
ACWI: annualized_mean_return=0.4536, daily_std=0.0064
IGOV: annualized_mean_return=0.1764, daily_std=0.0061
Minimum required portfolio return (annualized): 0.2473
Market regime: sideways

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

Answer: w_ACWI=0.4680, w_IGOV=0.5320

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000037 - 0.000006) / (0.000041 + 0.000037 - 0.000012)
  Unconstrained: w_ACWI=0.4681
  After long-only clamp: w_ACWI=0.4681, w_IGOV=0.5319.


Question:
Assets: ^VIX, TLH
^VIX: annualized_mean_return=-0.5796, daily_std=0.0493
TLH: annualized_mean_return=-0.0504, daily_std=0.0064
Minimum required portfolio return (annualized): -0.0598
Market regime: bull

Compute portfolio weights (w_^VIX, w_TLH) 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_TLH=X.XXXX

Answer: w_^VIX=0.0178, w_TLH=0.9822

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000041 - -0.000051) / (0.002435 + 0.000041 - -0.000103)
  Unconstrained: w_^VIX=0.0357
  After long-only clamp: w_^VIX=0.0357, w_TLH=0.9643.


Question:
Assets: ETH-USD, LQD
ETH-USD: annualized_mean_return=0.9576, daily_std=0.0264
LQD: annualized_mean_return=0.1008, daily_std=0.0064
Minimum required portfolio return (annualized): 0.1127
Market regime: sideways

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

Answer: w_ETH-USD=0.0283, w_LQD=0.9717

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000041 - 0.000021) / (0.000695 + 0.000041 - 0.000043)
  Unconstrained: w_ETH-USD=0.0277
  After long-only clamp: w_ETH-USD=0.0277, w_LQD=0.9723.


Question:
Assets: BNB-USD, ITB
BNB-USD: annualized_mean_return=0.2520, daily_std=0.0250
ITB: annualized_mean_return=-0.0756, daily_std=0.0155
Minimum required portfolio return (annualized): -0.0279
Market regime: sideways

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

Answer: w_BNB-USD=0.2865, w_ITB=0.7135

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000242 - -0.000017) / (0.000627 + 0.000242 - -0.000034)
  Unconstrained: w_BNB-USD=0.2864
  After long-only clamp: w_BNB-USD=0.2864, w_ITB=0.7136.


Question:
Assets: BNB-USD, VNQ
BNB-USD: annualized_mean_return=-0.2772, daily_std=0.0223
VNQ: annualized_mean_return=0.1260, daily_std=0.0101
Minimum required portfolio return (annualized): 0.0906
Market regime: sideways

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

Answer: w_BNB-USD=0.0878, w_VNQ=0.9122

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000101 - 0.000023) / (0.000497 + 0.000101 - 0.000046)
  Unconstrained: w_BNB-USD=0.1415
  After long-only clamp: w_BNB-USD=0.1415, w_VNQ=0.8585.


Question:
Assets: BTC-USD, USO
BTC-USD: annualized_mean_return=0.0252, daily_std=0.0243
USO: annualized_mean_return=-0.2268, daily_std=0.0194
Minimum required portfolio return (annualized): -0.0765
Market regime: sideways

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

Answer: w_BTC-USD=0.5964, w_USO=0.4036

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000377 - 0.000118) / (0.000592 + 0.000377 - 0.000236)
  Unconstrained: w_BTC-USD=0.3535
  After long-only clamp: w_BTC-USD=0.3535, w_USO=0.6465.


MATIC-USD σ=0.0442, SOYB σ=0.0095, ρ=-0.171. Min-variance weights: MATIC-USD=0.074, SOYB=0.926.

Question:
Assets: MATIC-USD, SOYB
MATIC-USD: annualized_mean_return=0.0504, daily_std=0.0442
SOYB: annualized_mean_return=-0.3024, daily_std=0.0095
Minimum required portfolio return (annualized): -0.0663
Market regime: sideways

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

Answer: w_MATIC-USD=0.6692, w_SOYB=0.3308

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000090 - -0.000072) / (0.001953 + 0.000090 - -0.000143)
  Unconstrained: w_MATIC-USD=0.0737
  After long-only clamp: w_MATIC-USD=0.0737, w_SOYB=0.9263.


ETH-USD σ=0.0383, ICSH σ=0.0002, ρ=0.007. Min-variance weights: ETH-USD=0.000, ICSH=1.000.

Question:
Assets: ETH-USD, ICSH
ETH-USD: annualized_mean_return=0.4788, daily_std=0.0383
ICSH: 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_ICSH) 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_ICSH=X.XXXX

Answer: w_ETH-USD=0.0000, w_ICSH=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.001463 + 0.000000 - 0.000000)
  Unconstrained: w_ETH-USD=-0.0000
  After long-only clamp: w_ETH-USD=0.0000, w_ICSH=1.0000.


Question:
Assets: XLU, USO
XLU: annualized_mean_return=-0.2016, daily_std=0.0089
USO: annualized_mean_return=0.3528, daily_std=0.0205
Minimum required portfolio return (annualized): 0.1685
Market regime: sideways

Compute portfolio weights (w_XLU, w_USO) 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_USO=X.XXXX

Answer: w_XLU=0.3324, w_USO=0.6676

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000422 - 0.000027) / (0.000080 + 0.000422 - 0.000054)
  Unconstrained: w_XLU=0.8816
  After long-only clamp: w_XLU=0.8816, w_USO=0.1184.


Question:
Assets: XLP, PPLT
XLP: annualized_mean_return=-0.1008, daily_std=0.0063
PPLT: annualized_mean_return=-0.5544, daily_std=0.0129
Minimum required portfolio return (annualized): -0.1227
Market regime: sideways

Compute portfolio weights (w_XLP, w_PPLT) 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_PPLT=X.XXXX

Answer: w_XLP=0.9517, w_PPLT=0.0483

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000165 - 0.000007) / (0.000039 + 0.000165 - 0.000014)
  Unconstrained: w_XLP=0.8310
  After long-only clamp: w_XLP=0.8310, w_PPLT=0.1690.


Question:
Assets: IWM, IYR
IWM: annualized_mean_return=0.2268, daily_std=0.0147
IYR: annualized_mean_return=0.2772, daily_std=0.0145
Minimum required portfolio return (annualized): 0.2634
Market regime: sideways

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

Answer: w_IWM=0.2738, w_IYR=0.7262

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000210 - 0.000183) / (0.000217 + 0.000210 - 0.000367)
  Unconstrained: w_IWM=0.4407
  After long-only clamp: w_IWM=0.4407, w_IYR=0.5593.


LINK-USD σ=0.0317, SHY σ=0.0011, ρ=0.082. Min-variance weights: LINK-USD=0.000, SHY=1.000.

Question:
Assets: LINK-USD, SHY
LINK-USD: annualized_mean_return=0.1008, daily_std=0.0317
SHY: annualized_mean_return=0.0504, daily_std=0.0011
Minimum required portfolio return (annualized): 0.0504
Market regime: sideways

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

Answer: w_LINK-USD=0.0000, w_SHY=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - 0.000003) / (0.001006 + 0.000001 - 0.000006)
  Unconstrained: w_LINK-USD=-0.0016
  After long-only clamp: w_LINK-USD=0.0000, w_SHY=1.0000.


BNB-USD σ=0.0262, PPLT σ=0.0165, ρ=0.080. Min-variance weights: BNB-USD=0.267, PPLT=0.733.

Question:
Assets: BNB-USD, PPLT
BNB-USD: annualized_mean_return=-0.2016, daily_std=0.0262
PPLT: annualized_mean_return=-0.1260, daily_std=0.0165
Minimum required portfolio return (annualized): -0.1398
Market regime: sideways

Compute portfolio weights (w_BNB-USD, w_PPLT) 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_PPLT=X.XXXX

Answer: w_BNB-USD=0.1825, w_PPLT=0.8175

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000273 - 0.000035) / (0.000689 + 0.000273 - 0.000070)
  Unconstrained: w_BNB-USD=0.2673
  After long-only clamp: w_BNB-USD=0.2673, w_PPLT=0.7327.


XRP-USD σ=0.0577, MTUM σ=0.0084, ρ=0.086. Min-variance weights: XRP-USD=0.009, MTUM=0.992.

Question:
Assets: XRP-USD, MTUM
XRP-USD: annualized_mean_return=4.0572, daily_std=0.0577
MTUM: annualized_mean_return=0.5292, daily_std=0.0084
Minimum required portfolio return (annualized): 0.5570
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_MTUM) 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_MTUM=X.XXXX

Answer: w_XRP-USD=0.0084, w_MTUM=0.9916

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000070 - 0.000042) / (0.003333 + 0.000070 - 0.000083)
  Unconstrained: w_XRP-USD=0.0085
  After long-only clamp: w_XRP-USD=0.0085, w_MTUM=0.9915.


Question:
Assets: XLK, VNQ
XLK: annualized_mean_return=-0.0000, daily_std=0.0154
VNQ: annualized_mean_return=0.5040, daily_std=0.0089
Minimum required portfolio return (annualized): 0.4550
Market regime: sideways

Compute portfolio weights (w_XLK, w_VNQ) 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_VNQ=X.XXXX

Answer: w_XLK=0.0972, w_VNQ=0.9028

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000079 - -0.000010) / (0.000237 + 0.000079 - -0.000020)
  Unconstrained: w_XLK=0.2645
  After long-only clamp: w_XLK=0.2645, w_VNQ=0.7355.


Question:
Assets: XLI, IGOV
XLI: annualized_mean_return=0.2268, daily_std=0.0100
IGOV: annualized_mean_return=0.2268, daily_std=0.0052
Minimum required portfolio return (annualized): 0.2268
Market regime: bull

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

Answer: w_XLI=0.2096, w_IGOV=0.7904

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000027 - 0.000001) / (0.000099 + 0.000027 - 0.000002)
  Unconstrained: w_XLI=0.2087
  After long-only clamp: w_XLI=0.2087, w_IGOV=0.7913.


Question:
Assets: MTUM, INDS
MTUM: annualized_mean_return=-0.0252, daily_std=0.0150
INDS: annualized_mean_return=0.4032, daily_std=0.0106
Minimum required portfolio return (annualized): 0.3619
Market regime: sideways

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

Answer: w_MTUM=0.0964, w_INDS=0.9036

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000113 - 0.000053) / (0.000224 + 0.000113 - 0.000106)
  Unconstrained: w_MTUM=0.2596
  After long-only clamp: w_MTUM=0.2596, w_INDS=0.7404.