Question:
Assets: XLY, XHB
XLY: annualized_mean_return=-0.2016, daily_std=0.0111
XHB: annualized_mean_return=0.0504, daily_std=0.0109
Minimum required portfolio return (annualized): -0.0983
Market regime: sideways

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

Answer: w_XLY=0.4463, w_XHB=0.5537

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000120 - 0.000103) / (0.000124 + 0.000120 - 0.000206)
  Unconstrained: w_XLY=0.4467
  After long-only clamp: w_XLY=0.4467, w_XHB=0.5533.


MATIC-USD σ=0.0783, QQQ σ=0.0225, ρ=-0.230. Min-variance weights: MATIC-USD=0.123, QQQ=0.877.

Question:
Assets: MATIC-USD, QQQ
MATIC-USD: annualized_mean_return=2.3184, daily_std=0.0783
QQQ: annualized_mean_return=-0.3276, daily_std=0.0225
Minimum required portfolio return (annualized): 1.2625
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_QQQ) 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_QQQ=X.XXXX

Answer: w_MATIC-USD=0.6009, w_QQQ=0.3991

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000508 - -0.000406) / (0.006131 + 0.000508 - -0.000812)
  Unconstrained: w_MATIC-USD=0.1227
  After long-only clamp: w_MATIC-USD=0.1227, w_QQQ=0.8773.


Question:
Assets: EWJ, BIL
EWJ: annualized_mean_return=0.0252, daily_std=0.0097
BIL: annualized_mean_return=-0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): -0.0000
Market regime: sideways

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

Answer: w_EWJ=0.0001, w_BIL=0.9999

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000095 + 0.000000 - -0.000000)
  Unconstrained: w_EWJ=0.0014
  After long-only clamp: w_EWJ=0.0014, w_BIL=0.9986.


Question:
Assets: BTC-USD, ITB
BTC-USD: annualized_mean_return=1.3356, daily_std=0.0354
ITB: annualized_mean_return=0.0504, daily_std=0.0108
Minimum required portfolio return (annualized): 0.5181
Market regime: sideways

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

Answer: w_BTC-USD=0.3639, w_ITB=0.6361

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000117 - 0.000039) / (0.001256 + 0.000117 - 0.000078)
  Unconstrained: w_BTC-USD=0.0604
  After long-only clamp: w_BTC-USD=0.0604, w_ITB=0.9396.


MATIC-USD σ=0.0701, ACWI σ=0.0069, ρ=-0.038. Min-variance weights: MATIC-USD=0.013, ACWI=0.987.

Question:
Assets: MATIC-USD, ACWI
MATIC-USD: annualized_mean_return=0.5292, daily_std=0.0701
ACWI: annualized_mean_return=-0.0504, daily_std=0.0069
Minimum required portfolio return (annualized): 0.2442
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_ACWI) 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_ACWI=X.XXXX

Answer: w_MATIC-USD=0.5083, w_ACWI=0.4917

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000047 - -0.000018) / (0.004915 + 0.000047 - -0.000037)
  Unconstrained: w_MATIC-USD=0.0131
  After long-only clamp: w_MATIC-USD=0.0131, w_ACWI=0.9869.


Question:
Assets: XLK, AVAX-USD
XLK: annualized_mean_return=-0.2520, daily_std=0.0160
AVAX-USD: annualized_mean_return=-0.4536, daily_std=0.0634
Minimum required portfolio return (annualized): -0.3368
Market regime: sideways

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

Answer: w_XLK=0.9040, w_AVAX-USD=0.0960

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.004024 - -0.000193) / (0.000255 + 0.004024 - -0.000386)
  Unconstrained: w_XLK=0.9040
  After long-only clamp: w_XLK=0.9040, w_AVAX-USD=0.0960.


Question:
Assets: ADA-USD, MTUM
ADA-USD: annualized_mean_return=-0.2772, daily_std=0.0648
MTUM: annualized_mean_return=-0.6552, daily_std=0.0220
Minimum required portfolio return (annualized): -0.5204
Market regime: sideways

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

Answer: w_ADA-USD=0.3566, w_MTUM=0.6434

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000485 - -0.000062) / (0.004193 + 0.000485 - -0.000124)
  Unconstrained: w_ADA-USD=0.1139
  After long-only clamp: w_ADA-USD=0.1139, w_MTUM=0.8861.


Question:
Assets: XRP-USD, HAUZ
XRP-USD: annualized_mean_return=0.7560, daily_std=0.0342
HAUZ: annualized_mean_return=-0.2520, daily_std=0.0109
Minimum required portfolio return (annualized): -0.2079
Market regime: sideways

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

Answer: w_XRP-USD=0.1091, w_HAUZ=0.8909

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000118 - -0.000029) / (0.001171 + 0.000118 - -0.000057)
  Unconstrained: w_XRP-USD=0.1089
  After long-only clamp: w_XRP-USD=0.1089, w_HAUZ=0.8911.


Question:
Assets: QUAL, SCHH
QUAL: annualized_mean_return=0.0504, daily_std=0.0079
SCHH: annualized_mean_return=0.0756, daily_std=0.0094
Minimum required portfolio return (annualized): 0.0710
Market regime: sideways

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

Answer: w_QUAL=0.1825, w_SCHH=0.8175

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000089 - 0.000048) / (0.000062 + 0.000089 - 0.000095)
  Unconstrained: w_QUAL=0.7371
  After long-only clamp: w_QUAL=0.7371, w_SCHH=0.2629.


Question:
Assets: FXI, ICSH
FXI: annualized_mean_return=-0.3276, daily_std=0.0109
ICSH: annualized_mean_return=0.0252, daily_std=0.0003
Minimum required portfolio return (annualized): -0.1446
Market regime: sideways

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

Answer: w_FXI=0.0088, w_ICSH=0.9912

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000001) / (0.000120 + 0.000000 - -0.000002)
  Unconstrained: w_FXI=0.0076
  After long-only clamp: w_FXI=0.0076, w_ICSH=0.9924.


Question:
Assets: MTUM, TLH
MTUM: annualized_mean_return=0.0756, daily_std=0.0066
TLH: annualized_mean_return=-0.1764, daily_std=0.0045
Minimum required portfolio return (annualized): 0.0384
Market regime: sideways

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

Answer: w_MTUM=0.8524, w_TLH=0.1476

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000020 - -0.000010) / (0.000044 + 0.000020 - -0.000020)
  Unconstrained: w_MTUM=0.3605
  After long-only clamp: w_MTUM=0.3605, w_TLH=0.6395.


Question:
Assets: XLK, IGOV
XLK: annualized_mean_return=-0.4284, daily_std=0.0124
IGOV: annualized_mean_return=0.0756, daily_std=0.0058
Minimum required portfolio return (annualized): -0.1194
Market regime: sideways

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

Answer: w_XLK=0.2596, w_IGOV=0.7404

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000033 - -0.000031) / (0.000153 + 0.000033 - -0.000062)
  Unconstrained: w_XLK=0.2591
  After long-only clamp: w_XLK=0.2591, w_IGOV=0.7409.


Question:
Assets: BNB-USD, FXI
BNB-USD: annualized_mean_return=0.6552, daily_std=0.0425
FXI: annualized_mean_return=0.3024, daily_std=0.0125
Minimum required portfolio return (annualized): 0.3974
Market regime: sideways

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

Answer: w_BNB-USD=0.2693, w_FXI=0.7307

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000157 - -0.000009) / (0.001802 + 0.000157 - -0.000018)
  Unconstrained: w_BNB-USD=0.0841
  After long-only clamp: w_BNB-USD=0.0841, w_FXI=0.9159.


Question:
Assets: ETH-USD, IEF
ETH-USD: annualized_mean_return=2.2176, daily_std=0.0437
IEF: annualized_mean_return=0.1008, daily_std=0.0031
Minimum required portfolio return (annualized): 0.1008
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=0.0000, w_IEF=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000009 - 0.000045) / (0.001906 + 0.000009 - 0.000091)
  Unconstrained: w_ETH-USD=-0.0197
  After long-only clamp: w_ETH-USD=0.0000, w_IEF=1.0000.


MATIC-USD σ=0.0794, TLH σ=0.0097, ρ=0.019. Min-variance weights: MATIC-USD=0.013, TLH=0.988.

Question:
Assets: MATIC-USD, TLH
MATIC-USD: annualized_mean_return=3.0996, daily_std=0.0794
TLH: annualized_mean_return=0.1008, daily_std=0.0097
Minimum required portfolio return (annualized): 1.7382
Market regime: sideways

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

Answer: w_MATIC-USD=0.5460, w_TLH=0.4540

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000095 - 0.000015) / (0.006301 + 0.000095 - 0.000030)
  Unconstrained: w_MATIC-USD=0.0125
  After long-only clamp: w_MATIC-USD=0.0125, w_TLH=0.9875.


Question:
Assets: ^VIX, BIL
^VIX: annualized_mean_return=0.6552, daily_std=0.0806
BIL: annualized_mean_return=0.0252, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0252
Market regime: sideways

Compute portfolio weights (w_^VIX, w_BIL) 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_BIL=X.XXXX

Answer: w_^VIX=0.0000, w_BIL=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000002) / (0.006504 + 0.000000 - 0.000004)
  Unconstrained: w_^VIX=-0.0003
  After long-only clamp: w_^VIX=0.0000, w_BIL=1.0000.


Question:
Assets: MTUM, PALL
MTUM: annualized_mean_return=0.4536, daily_std=0.0076
PALL: annualized_mean_return=0.6804, daily_std=0.0178
Minimum required portfolio return (annualized): 0.6305
Market regime: sideways

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

Answer: w_MTUM=0.2200, w_PALL=0.7800

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000318 - -0.000014) / (0.000058 + 0.000318 - -0.000028)
  Unconstrained: w_MTUM=0.8228
  After long-only clamp: w_MTUM=0.8228, w_PALL=0.1772.


Question:
Assets: EEM, TIP
EEM: annualized_mean_return=-0.0756, daily_std=0.0104
TIP: annualized_mean_return=0.0000, daily_std=0.0010
Minimum required portfolio return (annualized): -0.0283
Market regime: sideways

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

Answer: w_EEM=0.0096, w_TIP=0.9904

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - -0.000000) / (0.000108 + 0.000001 - -0.000000)
  Unconstrained: w_EEM=0.0114
  After long-only clamp: w_EEM=0.0114, w_TIP=0.9886.


Question:
Assets: XLK, TLH
XLK: annualized_mean_return=0.3780, daily_std=0.0071
TLH: annualized_mean_return=-0.1008, daily_std=0.0033
Minimum required portfolio return (annualized): 0.1045
Market regime: sideways

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

Answer: w_XLK=0.4288, w_TLH=0.5712

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000011 - -0.000007) / (0.000051 + 0.000011 - -0.000013)
  Unconstrained: w_XLK=0.2318
  After long-only clamp: w_XLK=0.2318, w_TLH=0.7682.


Question:
Assets: BNB-USD, VNQI
BNB-USD: annualized_mean_return=1.7640, daily_std=0.0404
VNQI: annualized_mean_return=-0.3024, daily_std=0.0170
Minimum required portfolio return (annualized): 0.1142
Market regime: sideways

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

Answer: w_BNB-USD=0.2198, w_VNQI=0.7802

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000291 - -0.000237) / (0.001635 + 0.000291 - -0.000473)
  Unconstrained: w_BNB-USD=0.2198
  After long-only clamp: w_BNB-USD=0.2198, w_VNQI=0.7802.


Question:
Assets: QQQ, INDS
QQQ: annualized_mean_return=0.1008, daily_std=0.0116
INDS: annualized_mean_return=0.2268, daily_std=0.0089
Minimum required portfolio return (annualized): 0.2024
Market regime: sideways

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

Answer: w_QQQ=0.0956, w_INDS=0.9044

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000079 - 0.000072) / (0.000134 + 0.000079 - 0.000144)
  Unconstrained: w_QQQ=0.0966
  After long-only clamp: w_QQQ=0.0966, w_INDS=0.9034.


Question:
Assets: QQQ, DBC
QQQ: annualized_mean_return=0.2016, daily_std=0.0075
DBC: annualized_mean_return=0.0756, daily_std=0.0094
Minimum required portfolio return (annualized): 0.1743
Market regime: sideways

Compute portfolio weights (w_QQQ, w_DBC) 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_DBC=X.XXXX

Answer: w_QQQ=0.7833, w_DBC=0.2167

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000089 - 0.000000) / (0.000057 + 0.000089 - 0.000000)
  Unconstrained: w_QQQ=0.6100
  After long-only clamp: w_QQQ=0.6100, w_DBC=0.3900.


Question:
Assets: BTC-USD, IEF
BTC-USD: annualized_mean_return=1.2600, daily_std=0.0628
IEF: annualized_mean_return=-0.0252, daily_std=0.0022
Minimum required portfolio return (annualized): -0.0252
Market regime: sideways

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

Answer: w_BTC-USD=0.0000, w_IEF=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000005 - 0.000017) / (0.003941 + 0.000005 - 0.000035)
  Unconstrained: w_BTC-USD=-0.0032
  After long-only clamp: w_BTC-USD=0.0000, w_IEF=1.0000.


Question:
Assets: DOT-USD, BIL
DOT-USD: annualized_mean_return=-2.5956, daily_std=0.0863
BIL: annualized_mean_return=0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): -0.0002
Market regime: sideways

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

Answer: w_DOT-USD=0.0001, w_BIL=0.9999

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000001) / (0.007452 + 0.000000 - -0.000003)
  Unconstrained: w_DOT-USD=0.0002
  After long-only clamp: w_DOT-USD=0.0002, w_BIL=0.9998.


ETH-USD σ=0.0522, WEAT σ=0.0150, ρ=0.164. Min-variance weights: ETH-USD=0.036, WEAT=0.964.

Question:
Assets: ETH-USD, WEAT
ETH-USD: annualized_mean_return=-1.2096, daily_std=0.0522
WEAT: annualized_mean_return=-0.0504, daily_std=0.0150
Minimum required portfolio return (annualized): -0.3232
Market regime: sideways

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

Answer: w_ETH-USD=0.0360, w_WEAT=0.9640

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000226 - 0.000129) / (0.002728 + 0.000226 - 0.000257)
  Unconstrained: w_ETH-USD=0.0361
  After long-only clamp: w_ETH-USD=0.0361, w_WEAT=0.9639.


Question:
Assets: USMV, TLT
USMV: annualized_mean_return=-0.2268, daily_std=0.0098
TLT: annualized_mean_return=-0.5040, daily_std=0.0114
Minimum required portfolio return (annualized): -0.2751
Market regime: sideways

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

Answer: w_USMV=0.8258, w_TLT=0.1742

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000130 - -0.000013) / (0.000097 + 0.000130 - -0.000027)
  Unconstrained: w_USMV=0.5668
  After long-only clamp: w_USMV=0.5668, w_TLT=0.4332.


Question:
Assets: BNB-USD, BNO
BNB-USD: annualized_mean_return=2.5704, daily_std=0.0856
BNO: annualized_mean_return=0.2772, daily_std=0.0214
Minimum required portfolio return (annualized): 0.4397
Market regime: sideways

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

Answer: w_BNB-USD=0.0803, w_BNO=0.9197

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000457 - -0.000201) / (0.007332 + 0.000457 - -0.000401)
  Unconstrained: w_BNB-USD=0.0803
  After long-only clamp: w_BNB-USD=0.0803, w_BNO=0.9197.


Question:
Assets: FXI, MORT
FXI: annualized_mean_return=-0.1260, daily_std=0.0162
MORT: annualized_mean_return=0.2268, daily_std=0.0080
Minimum required portfolio return (annualized): 0.0397
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=0.0289, w_MORT=0.9711

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000064 - 0.000058) / (0.000264 + 0.000064 - 0.000117)
  Unconstrained: w_FXI=0.0270
  After long-only clamp: w_FXI=0.0270, w_MORT=0.9730.


Question:
Assets: XLK, DBC
XLK: annualized_mean_return=0.2268, daily_std=0.0102
DBC: annualized_mean_return=0.1260, daily_std=0.0109
Minimum required portfolio return (annualized): 0.1696
Market regime: sideways

Compute portfolio weights (w_XLK, w_DBC) 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_DBC=X.XXXX

Answer: w_XLK=0.5408, w_DBC=0.4592

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000119 - 0.000015) / (0.000103 + 0.000119 - 0.000030)
  Unconstrained: w_XLK=0.5409
  After long-only clamp: w_XLK=0.5409, w_DBC=0.4591.


BTC-USD σ=0.0531, SCHP σ=0.0024, ρ=0.095. Min-variance weights: BTC-USD=0.000, SCHP=1.000.

Question:
Assets: BTC-USD, SCHP
BTC-USD: annualized_mean_return=1.5624, daily_std=0.0531
SCHP: annualized_mean_return=0.1512, daily_std=0.0024
Minimum required portfolio return (annualized): 0.1512
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_SCHP) 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_SCHP=X.XXXX

Answer: w_BTC-USD=0.0000, w_SCHP=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000006 - 0.000012) / (0.002818 + 0.000006 - 0.000024)
  Unconstrained: w_BTC-USD=-0.0023
  After long-only clamp: w_BTC-USD=0.0000, w_SCHP=1.0000.


ADA-USD σ=0.0864, HAUZ σ=0.0074, ρ=0.250. Min-variance weights: ADA-USD=0.000, HAUZ=1.000.

Question:
Assets: ADA-USD, HAUZ
ADA-USD: annualized_mean_return=1.3860, daily_std=0.0864
HAUZ: annualized_mean_return=0.2268, daily_std=0.0074
Minimum required portfolio return (annualized): 0.2268
Market regime: sideways

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

Answer: w_ADA-USD=0.0000, w_HAUZ=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000055 - 0.000160) / (0.007470 + 0.000055 - 0.000320)
  Unconstrained: w_ADA-USD=-0.0146
  After long-only clamp: w_ADA-USD=0.0000, w_HAUZ=1.0000.


Question:
Assets: LINK-USD, IYR
LINK-USD: annualized_mean_return=2.1420, daily_std=0.0818
IYR: annualized_mean_return=0.2016, daily_std=0.0122
Minimum required portfolio return (annualized): 0.2437
Market regime: sideways

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

Answer: w_LINK-USD=0.0364, w_IYR=0.9636

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000148 - -0.000108) / (0.006686 + 0.000148 - -0.000216)
  Unconstrained: w_LINK-USD=0.0364
  After long-only clamp: w_LINK-USD=0.0364, w_IYR=0.9636.


Question:
Assets: XRP-USD, SOYB
XRP-USD: annualized_mean_return=2.1420, daily_std=0.0991
SOYB: annualized_mean_return=0.6048, daily_std=0.0118
Minimum required portfolio return (annualized): 0.6337
Market regime: sideways

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

Answer: w_XRP-USD=0.0190, w_SOYB=0.9810

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000139 - -0.000052) / (0.009822 + 0.000139 - -0.000104)
  Unconstrained: w_XRP-USD=0.0189
  After long-only clamp: w_XRP-USD=0.0189, w_SOYB=0.9811.


Question:
Assets: ADA-USD, DBA
ADA-USD: annualized_mean_return=-1.5120, daily_std=0.0519
DBA: annualized_mean_return=-0.2268, daily_std=0.0084
Minimum required portfolio return (annualized): -0.9776
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=0.0375, w_DBA=0.9625

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000071 - -0.000035) / (0.002690 + 0.000071 - -0.000070)
  Unconstrained: w_ADA-USD=0.0375
  After long-only clamp: w_ADA-USD=0.0375, w_DBA=0.9625.


Question:
Assets: USMV, HAUZ
USMV: annualized_mean_return=-0.2772, daily_std=0.0116
HAUZ: annualized_mean_return=-0.7056, daily_std=0.0131
Minimum required portfolio return (annualized): -0.4966
Market regime: sideways

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

Answer: w_USMV=0.7461, w_HAUZ=0.2539

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000171 - 0.000114) / (0.000134 + 0.000171 - 0.000229)
  Unconstrained: w_USMV=0.7480
  After long-only clamp: w_USMV=0.7480, w_HAUZ=0.2520.


Question:
Assets: VEA, XHB
VEA: annualized_mean_return=0.1008, daily_std=0.0051
XHB: annualized_mean_return=0.0504, daily_std=0.0076
Minimum required portfolio return (annualized): 0.0988
Market regime: sideways

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

Answer: w_VEA=0.9603, w_XHB=0.0397

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000058 - 0.000023) / (0.000026 + 0.000058 - 0.000046)
  Unconstrained: w_VEA=0.9252
  After long-only clamp: w_VEA=0.9252, w_XHB=0.0748.


Question:
Assets: XRP-USD, BIL
XRP-USD: annualized_mean_return=-2.9484, daily_std=0.0507
BIL: annualized_mean_return=-0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): -0.9996
Market regime: sideways

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

Answer: w_XRP-USD=0.0000, w_BIL=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.002575 + 0.000000 - 0.000001)
  Unconstrained: w_XRP-USD=-0.0003
  After long-only clamp: w_XRP-USD=0.0000, w_BIL=1.0000.


Question:
Assets: BTC-USD, BIL
BTC-USD: annualized_mean_return=0.0252, daily_std=0.0274
BIL: annualized_mean_return=-0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0079
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=0.3135, w_BIL=0.6865

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000751 + 0.000000 - 0.000001)
  Unconstrained: w_BTC-USD=-0.0004
  After long-only clamp: w_BTC-USD=0.0000, w_BIL=1.0000.


Question:
Assets: XLF, BIL
XLF: annualized_mean_return=0.0756, daily_std=0.0089
BIL: annualized_mean_return=0.0252, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0527
Market regime: sideways

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

Answer: w_XLF=0.5456, w_BIL=0.4544

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000080 + 0.000000 - -0.000001)
  Unconstrained: w_XLF=0.0034
  After long-only clamp: w_XLF=0.0034, w_BIL=0.9966.


Question:
Assets: BTC-USD, ICSH
BTC-USD: annualized_mean_return=2.1168, daily_std=0.0309
ICSH: annualized_mean_return=-0.0000, daily_std=0.0002
Minimum required portfolio return (annualized): 0.9743
Market regime: sideways

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

Answer: w_BTC-USD=0.4603, w_ICSH=0.5397

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000952 + 0.000000 - -0.000000)
  Unconstrained: w_BTC-USD=0.0003
  After long-only clamp: w_BTC-USD=0.0003, w_ICSH=0.9997.


Question:
Assets: VTI, ICSH
VTI: annualized_mean_return=0.1764, daily_std=0.0044
ICSH: annualized_mean_return=0.0252, daily_std=0.0011
Minimum required portfolio return (annualized): 0.1414
Market regime: sideways

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

Answer: w_VTI=0.7685, w_ICSH=0.2315

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - -0.000000) / (0.000019 + 0.000001 - -0.000000)
  Unconstrained: w_VTI=0.0620
  After long-only clamp: w_VTI=0.0620, w_ICSH=0.9380.


BTC-USD σ=0.0358, MORT σ=0.0077, ρ=0.032. Min-variance weights: BTC-USD=0.038, MORT=0.962.

Question:
Assets: BTC-USD, MORT
BTC-USD: annualized_mean_return=1.4364, daily_std=0.0358
MORT: annualized_mean_return=0.2520, daily_std=0.0077
Minimum required portfolio return (annualized): 1.0552
Market regime: sideways

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

Answer: w_BTC-USD=0.6781, w_MORT=0.3219

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000059 - 0.000009) / (0.001282 + 0.000059 - 0.000017)
  Unconstrained: w_BTC-USD=0.0379
  After long-only clamp: w_BTC-USD=0.0379, w_MORT=0.9621.


Question:
Assets: XRP-USD, BIL
XRP-USD: annualized_mean_return=-1.8900, daily_std=0.0277
BIL: annualized_mean_return=0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0000
Market regime: sideways

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

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

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000769 + 0.000000 - -0.000000)
  Unconstrained: w_XRP-USD=0.0000
  After long-only clamp: w_XRP-USD=0.0000, w_BIL=1.0000.


MATIC-USD σ=0.0626, SCHP σ=0.0053, ρ=0.147. Min-variance weights: MATIC-USD=0.000, SCHP=1.000.

Question:
Assets: MATIC-USD, SCHP
MATIC-USD: annualized_mean_return=-2.9232, daily_std=0.0626
SCHP: annualized_mean_return=-0.2520, daily_std=0.0053
Minimum required portfolio return (annualized): -1.2072
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_SCHP) 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_SCHP=X.XXXX

Answer: w_MATIC-USD=0.0000, w_SCHP=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000028 - 0.000049) / (0.003916 + 0.000028 - 0.000097)
  Unconstrained: w_MATIC-USD=-0.0054
  After long-only clamp: w_MATIC-USD=0.0000, w_SCHP=1.0000.


Question:
Assets: EFA, SHV
EFA: annualized_mean_return=-0.0504, daily_std=0.0139
SHV: annualized_mean_return=0.0252, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0003
Market regime: sideways

Compute portfolio weights (w_EFA, w_SHV) 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_SHV=X.XXXX

Answer: w_EFA=0.0000, w_SHV=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.000194 + 0.000000 - 0.000001)
  Unconstrained: w_EFA=-0.0026
  After long-only clamp: w_EFA=0.0000, w_SHV=1.0000.


Question:
Assets: VTI, BTC-USD
VTI: annualized_mean_return=0.1512, daily_std=0.0050
BTC-USD: annualized_mean_return=-0.0252, daily_std=0.0322
Minimum required portfolio return (annualized): 0.1190
Market regime: sideways

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

Answer: w_VTI=0.9718, w_BTC-USD=0.0282

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.001039 - -0.000005) / (0.000025 + 0.001039 - -0.000010)
  Unconstrained: w_VTI=0.9718
  After long-only clamp: w_VTI=0.9718, w_BTC-USD=0.0282.


Question:
Assets: EFA, VCIT
EFA: annualized_mean_return=-0.2520, daily_std=0.0127
VCIT: annualized_mean_return=0.0756, daily_std=0.0028
Minimum required portfolio return (annualized): -0.0101
Market regime: sideways

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

Answer: w_EFA=0.0619, w_VCIT=0.9381

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000008 - -0.000003) / (0.000162 + 0.000008 - -0.000006)
  Unconstrained: w_EFA=0.0621
  After long-only clamp: w_EFA=0.0621, w_VCIT=0.9379.


Question:
Assets: QQQ, HYG
QQQ: annualized_mean_return=-0.1260, daily_std=0.0184
HYG: annualized_mean_return=0.1260, daily_std=0.0076
Minimum required portfolio return (annualized): 0.0790
Market regime: sideways

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

Answer: w_QQQ=0.0539, w_HYG=0.9461

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000058 - 0.000041) / (0.000337 + 0.000058 - 0.000083)
  Unconstrained: w_QQQ=0.0526
  After long-only clamp: w_QQQ=0.0526, w_HYG=0.9474.


Question:
Assets: EEM, MORT
EEM: annualized_mean_return=0.1764, daily_std=0.0123
MORT: annualized_mean_return=0.1008, daily_std=0.0103
Minimum required portfolio return (annualized): 0.1237
Market regime: sideways

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

Answer: w_EEM=0.3726, w_MORT=0.6274

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000107 - 0.000041) / (0.000151 + 0.000107 - 0.000083)
  Unconstrained: w_EEM=0.3721
  After long-only clamp: w_EEM=0.3721, w_MORT=0.6279.


Question:
Assets: XLI, ICSH
XLI: annualized_mean_return=0.1260, daily_std=0.0089
ICSH: annualized_mean_return=0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0819
Market regime: sideways

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

Answer: w_XLI=0.6500, w_ICSH=0.3500

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000078 + 0.000000 - 0.000001)
  Unconstrained: w_XLI=-0.0035
  After long-only clamp: w_XLI=0.0000, w_ICSH=1.0000.


Question:
Assets: XLY, TLT
XLY: annualized_mean_return=-1.0080, daily_std=0.0231
TLT: annualized_mean_return=-0.3528, daily_std=0.0122
Minimum required portfolio return (annualized): -0.4467
Market regime: sideways

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

Answer: w_XLY=0.1433, w_TLT=0.8567

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000149 - -0.000033) / (0.000533 + 0.000149 - -0.000066)
  Unconstrained: w_XLY=0.2428
  After long-only clamp: w_XLY=0.2428, w_TLT=0.7572.


Question:
Assets: VTI, JNK
VTI: annualized_mean_return=0.1008, daily_std=0.0096
JNK: annualized_mean_return=-0.0252, daily_std=0.0030
Minimum required portfolio return (annualized): 0.0093
Market regime: sideways

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

Answer: w_VTI=0.2738, w_JNK=0.7262

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000009 - 0.000009) / (0.000091 + 0.000009 - 0.000018)
  Unconstrained: w_VTI=0.0052
  After long-only clamp: w_VTI=0.0052, w_JNK=0.9948.


Question:
Assets: XRP-USD, SCHH
XRP-USD: annualized_mean_return=0.6804, daily_std=0.0969
SCHH: annualized_mean_return=0.4032, daily_std=0.0116
Minimum required portfolio return (annualized): 0.5500
Market regime: sideways

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

Answer: w_XRP-USD=0.5296, w_SCHH=0.4704

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000135 - -0.000055) / (0.009388 + 0.000135 - -0.000109)
  Unconstrained: w_XRP-USD=0.0197
  After long-only clamp: w_XRP-USD=0.0197, w_SCHH=0.9803.


Question:
Assets: IVV, SCHH
IVV: annualized_mean_return=-0.1260, daily_std=0.0097
SCHH: annualized_mean_return=-0.0252, daily_std=0.0106
Minimum required portfolio return (annualized): -0.0764
Market regime: sideways

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

Answer: w_IVV=0.5079, w_SCHH=0.4921

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000112 - 0.000077) / (0.000094 + 0.000112 - 0.000154)
  Unconstrained: w_IVV=0.6771
  After long-only clamp: w_IVV=0.6771, w_SCHH=0.3229.


Question:
Assets: ACWI, XHB
ACWI: annualized_mean_return=0.2268, daily_std=0.0097
XHB: annualized_mean_return=0.8568, daily_std=0.0155
Minimum required portfolio return (annualized): 0.3532
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=0.7994, w_XHB=0.2006

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000239 - 0.000117) / (0.000093 + 0.000239 - 0.000235)
  Unconstrained: w_ACWI=1.2472
  After long-only clamp: w_ACWI=1.0000, w_XHB=0.0000.


Question:
Assets: IVV, ITB
IVV: annualized_mean_return=-0.2268, daily_std=0.0136
ITB: annualized_mean_return=-1.1592, daily_std=0.0233
Minimum required portfolio return (annualized): -0.2702
Market regime: sideways

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

Answer: w_IVV=1.0000, w_ITB=0.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000541 - 0.000249) / (0.000185 + 0.000541 - 0.000498)
  Unconstrained: w_IVV=1.2810
  After long-only clamp: w_IVV=1.0000, w_ITB=0.0000.


Question:
Assets: SOL-USD, SCHH
SOL-USD: annualized_mean_return=3.0996, daily_std=0.0677
SCHH: annualized_mean_return=0.1008, daily_std=0.0084
Minimum required portfolio return (annualized): 1.6529
Market regime: sideways

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

Answer: w_SOL-USD=0.5176, w_SCHH=0.4824

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000070 - -0.000001) / (0.004583 + 0.000070 - -0.000003)
  Unconstrained: w_SOL-USD=0.0154
  After long-only clamp: w_SOL-USD=0.0154, w_SCHH=0.9846.


Question:
Assets: DOT-USD, PPLT
DOT-USD: annualized_mean_return=-0.3024, daily_std=0.0423
PPLT: annualized_mean_return=0.0756, daily_std=0.0174
Minimum required portfolio return (annualized): -0.0716
Market regime: sideways

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

Answer: w_DOT-USD=0.1463, w_PPLT=0.8537

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000303 - -0.000005) / (0.001793 + 0.000303 - -0.000011)
  Unconstrained: w_DOT-USD=0.1465
  After long-only clamp: w_DOT-USD=0.1465, w_PPLT=0.8535.


Question:
Assets: BNB-USD, REZ
BNB-USD: annualized_mean_return=-0.3276, daily_std=0.0278
REZ: annualized_mean_return=-0.2268, daily_std=0.0135
Minimum required portfolio return (annualized): -0.2426
Market regime: sideways

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

Answer: w_BNB-USD=0.1567, w_REZ=0.8433

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000181 - -0.000085) / (0.000772 + 0.000181 - -0.000170)
  Unconstrained: w_BNB-USD=0.2368
  After long-only clamp: w_BNB-USD=0.2368, w_REZ=0.7632.


Question:
Assets: ADA-USD, DBC
ADA-USD: annualized_mean_return=0.8316, daily_std=0.0507
DBC: annualized_mean_return=0.3528, daily_std=0.0097
Minimum required portfolio return (annualized): 0.7028
Market regime: sideways

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

Answer: w_ADA-USD=0.7310, w_DBC=0.2690

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000093 - 0.000015) / (0.002570 + 0.000093 - 0.000030)
  Unconstrained: w_ADA-USD=0.0297
  After long-only clamp: w_ADA-USD=0.0297, w_DBC=0.9703.


Question:
Assets: IWM, INDS
IWM: annualized_mean_return=0.2520, daily_std=0.0069
INDS: annualized_mean_return=0.1764, daily_std=0.0079
Minimum required portfolio return (annualized): 0.2411
Market regime: sideways

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

Answer: w_IWM=0.8558, w_INDS=0.1442

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000063 - 0.000018) / (0.000047 + 0.000063 - 0.000037)
  Unconstrained: w_IWM=0.6084
  After long-only clamp: w_IWM=0.6084, w_INDS=0.3916.


Question:
Assets: VEA, TLH
VEA: annualized_mean_return=0.2268, daily_std=0.0112
TLH: annualized_mean_return=-0.2520, daily_std=0.0062
Minimum required portfolio return (annualized): -0.1667
Market regime: sideways

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

Answer: w_VEA=0.2272, w_TLH=0.7728

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000038 - 0.000002) / (0.000125 + 0.000038 - 0.000005)
  Unconstrained: w_VEA=0.2261
  After long-only clamp: w_VEA=0.2261, w_TLH=0.7739.


Question:
Assets: XLP, IAU
XLP: annualized_mean_return=-0.1260, daily_std=0.0046
IAU: annualized_mean_return=0.0252, daily_std=0.0066
Minimum required portfolio return (annualized): -0.0808
Market regime: sideways

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

Answer: w_XLP=0.6687, w_IAU=0.3313

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000043 - 0.000000) / (0.000021 + 0.000043 - 0.000001)
  Unconstrained: w_XLP=0.6706
  After long-only clamp: w_XLP=0.6706, w_IAU=0.3294.


Question:
Assets: EFA, WEAT
EFA: annualized_mean_return=0.2016, daily_std=0.0047
WEAT: annualized_mean_return=0.0504, daily_std=0.0186
Minimum required portfolio return (annualized): 0.1960
Market regime: sideways

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

Answer: w_EFA=0.9630, w_WEAT=0.0370

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000345 - -0.000008) / (0.000022 + 0.000345 - -0.000017)
  Unconstrained: w_EFA=0.9213
  After long-only clamp: w_EFA=0.9213, w_WEAT=0.0787.


Question:
Assets: QQQ, ADA-USD
QQQ: annualized_mean_return=0.2772, daily_std=0.0233
ADA-USD: annualized_mean_return=3.7548, daily_std=0.0470
Minimum required portfolio return (annualized): 2.4987
Market regime: sideways

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

Answer: w_QQQ=0.3612, w_ADA-USD=0.6388

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.002209 - 0.000057) / (0.000545 + 0.002209 - 0.000114)
  Unconstrained: w_QQQ=0.8152
  After long-only clamp: w_QQQ=0.8152, w_ADA-USD=0.1848.


Question:
Assets: XLV, ICSH
XLV: annualized_mean_return=0.4284, daily_std=0.0133
ICSH: annualized_mean_return=0.0504, daily_std=0.0002
Minimum required portfolio return (annualized): 0.2896
Market regime: sideways

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

Answer: w_XLV=0.6328, w_ICSH=0.3672

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000001) / (0.000176 + 0.000000 - 0.000001)
  Unconstrained: w_XLV=-0.0030
  After long-only clamp: w_XLV=0.0000, w_ICSH=1.0000.


Question:
Assets: BNB-USD, ITB
BNB-USD: annualized_mean_return=-1.1844, daily_std=0.0645
ITB: annualized_mean_return=0.2268, daily_std=0.0193
Minimum required portfolio return (annualized): 0.2068
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=0.0142, w_ITB=0.9858

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000374 - 0.000145) / (0.004163 + 0.000374 - 0.000289)
  Unconstrained: w_BNB-USD=0.0539
  After long-only clamp: w_BNB-USD=0.0539, w_ITB=0.9461.


Question:
Assets: BTC-USD, GLD
BTC-USD: annualized_mean_return=3.7296, daily_std=0.0361
GLD: annualized_mean_return=0.0756, daily_std=0.0088
Minimum required portfolio return (annualized): 2.6039
Market regime: sideways

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

Answer: w_BTC-USD=0.6919, w_GLD=0.3081

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000078 - 0.000110) / (0.001301 + 0.000078 - 0.000220)
  Unconstrained: w_BTC-USD=-0.0274
  After long-only clamp: w_BTC-USD=0.0000, w_GLD=1.0000.


ETH-USD σ=0.0368, MORT σ=0.0039, ρ=0.125. Min-variance weights: ETH-USD=0.000, MORT=1.000.

Question:
Assets: ETH-USD, MORT
ETH-USD: annualized_mean_return=2.2176, daily_std=0.0368
MORT: annualized_mean_return=0.4032, daily_std=0.0039
Minimum required portfolio return (annualized): 1.7609
Market regime: sideways

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

Answer: w_ETH-USD=0.7483, w_MORT=0.2517

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000015 - 0.000018) / (0.001356 + 0.000015 - 0.000036)
  Unconstrained: w_ETH-USD=-0.0020
  After long-only clamp: w_ETH-USD=0.0000, w_MORT=1.0000.


Question:
Assets: XLP, GLD
XLP: annualized_mean_return=0.2268, daily_std=0.0092
GLD: annualized_mean_return=-0.2268, daily_std=0.0092
Minimum required portfolio return (annualized): 0.0498
Market regime: sideways

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

Answer: w_XLP=0.6098, w_GLD=0.3902

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000085 - 0.000020) / (0.000085 + 0.000085 - 0.000039)
  Unconstrained: w_XLP=0.5003
  After long-only clamp: w_XLP=0.5003, w_GLD=0.4997.


ADA-USD σ=0.0485, ICSH σ=0.0002, ρ=0.040. Min-variance weights: ADA-USD=0.000, ICSH=1.000.

Question:
Assets: ADA-USD, ICSH
ADA-USD: annualized_mean_return=-2.1168, daily_std=0.0485
ICSH: annualized_mean_return=0.0000, daily_std=0.0002
Minimum required portfolio return (annualized): -0.0000
Market regime: sideways

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

Answer: w_ADA-USD=0.0000, w_ICSH=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.002354 + 0.000000 - 0.000001)
  Unconstrained: w_ADA-USD=-0.0002
  After long-only clamp: w_ADA-USD=0.0000, w_ICSH=1.0000.


Question:
Assets: VTI, VNQI
VTI: annualized_mean_return=0.3276, daily_std=0.0111
VNQI: annualized_mean_return=0.1008, daily_std=0.0087
Minimum required portfolio return (annualized): 0.1208
Market regime: sideways

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

Answer: w_VTI=0.0918, w_VNQI=0.9082

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000075 - 0.000070) / (0.000122 + 0.000075 - 0.000139)
  Unconstrained: w_VTI=0.0962
  After long-only clamp: w_VTI=0.0962, w_VNQI=0.9038.


Question:
Assets: XLK, PDBC
XLK: annualized_mean_return=0.3780, daily_std=0.0043
PDBC: annualized_mean_return=-0.1512, daily_std=0.0071
Minimum required portfolio return (annualized): 0.0520
Market regime: sideways

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

Answer: w_XLK=0.7491, w_PDBC=0.2509

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000050 - 0.000003) / (0.000019 + 0.000050 - 0.000005)
  Unconstrained: w_XLK=0.7471
  After long-only clamp: w_XLK=0.7471, w_PDBC=0.2529.


Question:
Assets: ADA-USD, REZ
ADA-USD: annualized_mean_return=0.8568, daily_std=0.0491
REZ: annualized_mean_return=-0.0504, daily_std=0.0128
Minimum required portfolio return (annualized): -0.0198
Market regime: sideways

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

Answer: w_ADA-USD=0.0685, w_REZ=0.9315

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000164 - -0.000014) / (0.002411 + 0.000164 - -0.000028)
  Unconstrained: w_ADA-USD=0.0684
  After long-only clamp: w_ADA-USD=0.0684, w_REZ=0.9316.


Question:
Assets: FXI, PPLT
FXI: annualized_mean_return=0.7812, daily_std=0.0149
PPLT: annualized_mean_return=-0.2520, daily_std=0.0117
Minimum required portfolio return (annualized): -0.0139
Market regime: sideways

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

Answer: w_FXI=0.3802, w_PPLT=0.6198

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000136 - -0.000002) / (0.000223 + 0.000136 - -0.000004)
  Unconstrained: w_FXI=0.3801
  After long-only clamp: w_FXI=0.3801, w_PPLT=0.6199.


LINK-USD σ=0.0723, SCHH σ=0.0106, ρ=-0.091. Min-variance weights: LINK-USD=0.033, SCHH=0.967.

Question:
Assets: LINK-USD, SCHH
LINK-USD: annualized_mean_return=-0.7560, daily_std=0.0723
SCHH: annualized_mean_return=0.0252, daily_std=0.0106
Minimum required portfolio return (annualized): -0.3150
Market regime: sideways

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

Answer: w_LINK-USD=0.0334, w_SCHH=0.9666

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000113 - -0.000070) / (0.005228 + 0.000113 - -0.000140)
  Unconstrained: w_LINK-USD=0.0334
  After long-only clamp: w_LINK-USD=0.0334, w_SCHH=0.9666.


Question:
Assets: FXI, SOYB
FXI: annualized_mean_return=-0.2520, daily_std=0.0147
SOYB: annualized_mean_return=-0.1008, daily_std=0.0120
Minimum required portfolio return (annualized): -0.1994
Market regime: sideways

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

Answer: w_FXI=0.4048, w_SOYB=0.5952

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000145 - -0.000006) / (0.000216 + 0.000145 - -0.000011)
  Unconstrained: w_FXI=0.4046
  After long-only clamp: w_FXI=0.4046, w_SOYB=0.5954.


Question:
Assets: BTC-USD, VEA
BTC-USD: annualized_mean_return=-0.6048, daily_std=0.0283
VEA: annualized_mean_return=0.3528, daily_std=0.0058
Minimum required portfolio return (annualized): -0.1417
Market regime: sideways

Compute portfolio weights (w_BTC-USD, w_VEA) 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_VEA=X.XXXX

Answer: w_BTC-USD=0.0000, w_VEA=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000034 - 0.000056) / (0.000800 + 0.000034 - 0.000112)
  Unconstrained: w_BTC-USD=-0.0312
  After long-only clamp: w_BTC-USD=0.0000, w_VEA=1.0000.


Question:
Assets: DOT-USD, IWM
DOT-USD: annualized_mean_return=7.3836, daily_std=0.0998
IWM: annualized_mean_return=1.1592, daily_std=0.0127
Minimum required portfolio return (annualized): 1.1592
Market regime: sideways

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

Answer: w_DOT-USD=0.0000, w_IWM=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000162 - 0.000273) / (0.009957 + 0.000162 - 0.000546)
  Unconstrained: w_DOT-USD=-0.0115
  After long-only clamp: w_DOT-USD=0.0000, w_IWM=1.0000.


Question:
Assets: ETH-USD, REZ
ETH-USD: annualized_mean_return=-0.6552, daily_std=0.0405
REZ: annualized_mean_return=0.0252, daily_std=0.0108
Minimum required portfolio return (annualized): -0.3872
Market regime: sideways

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

Answer: w_ETH-USD=0.0876, w_REZ=0.9124

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000117 - -0.000045) / (0.001642 + 0.000117 - -0.000090)
  Unconstrained: w_ETH-USD=0.0876
  After long-only clamp: w_ETH-USD=0.0876, w_REZ=0.9124.


Question:
Assets: XLP, MORT
XLP: annualized_mean_return=0.2520, daily_std=0.0039
MORT: annualized_mean_return=0.3780, daily_std=0.0056
Minimum required portfolio return (annualized): 0.2759
Market regime: sideways

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

Answer: w_XLP=0.7499, w_MORT=0.2501

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000032 - 0.000007) / (0.000015 + 0.000032 - 0.000014)
  Unconstrained: w_XLP=0.7511
  After long-only clamp: w_XLP=0.7511, w_MORT=0.2489.


Question:
Assets: XLE, SGOV
XLE: annualized_mean_return=0.2016, daily_std=0.0248
SGOV: annualized_mean_return=0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): -0.0000
Market regime: sideways

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

Answer: w_XLE=0.0000, w_SGOV=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000614 + 0.000000 - 0.000000)
  Unconstrained: w_XLE=-0.0004
  After long-only clamp: w_XLE=0.0000, w_SGOV=1.0000.


Question:
Assets: XLV, TIP
XLV: annualized_mean_return=-0.0252, daily_std=0.0082
TIP: annualized_mean_return=0.0000, daily_std=0.0010
Minimum required portfolio return (annualized): -0.0064
Market regime: sideways

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

Answer: w_XLV=0.0417, w_TIP=0.9583

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000001 - -0.000002) / (0.000068 + 0.000001 - -0.000004)
  Unconstrained: w_XLV=0.0416
  After long-only clamp: w_XLV=0.0416, w_TIP=0.9584.


Question:
Assets: BTC-USD, BNO
BTC-USD: annualized_mean_return=-0.4284, daily_std=0.0273
BNO: annualized_mean_return=0.6552, daily_std=0.0260
Minimum required portfolio return (annualized): 0.3004
Market regime: sideways

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

Answer: w_BTC-USD=0.3274, w_BNO=0.6726

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000678 - 0.000150) / (0.000745 + 0.000678 - 0.000300)
  Unconstrained: w_BTC-USD=0.4704
  After long-only clamp: w_BTC-USD=0.4704, w_BNO=0.5296.


Question:
Assets: FXI, JNK
FXI: annualized_mean_return=-0.3024, daily_std=0.0116
JNK: annualized_mean_return=0.0756, daily_std=0.0030
Minimum required portfolio return (annualized): 0.0586
Market regime: sideways

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

Answer: w_FXI=0.0450, w_JNK=0.9550

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000009 - 0.000001) / (0.000133 + 0.000009 - 0.000002)
  Unconstrained: w_FXI=0.0575
  After long-only clamp: w_FXI=0.0575, w_JNK=0.9425.


Question:
Assets: EFA, BNO
EFA: annualized_mean_return=-0.5040, daily_std=0.0120
BNO: annualized_mean_return=2.1924, daily_std=0.0222
Minimum required portfolio return (annualized): 0.2624
Market regime: sideways

Compute portfolio weights (w_EFA, w_BNO) 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_BNO=X.XXXX

Answer: w_EFA=0.7098, w_BNO=0.2902

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000494 - -0.000098) / (0.000144 + 0.000494 - -0.000196)
  Unconstrained: w_EFA=0.7099
  After long-only clamp: w_EFA=0.7099, w_BNO=0.2901.


Question:
Assets: QUAL, SHV
QUAL: annualized_mean_return=0.3528, daily_std=0.0033
SHV: annualized_mean_return=0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): 0.0003
Market regime: sideways

Compute portfolio weights (w_QUAL, w_SHV) 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_SHV=X.XXXX

Answer: w_QUAL=0.0009, w_SHV=0.9991

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000011 + 0.000000 - -0.000000)
  Unconstrained: w_QUAL=0.0025
  After long-only clamp: w_QUAL=0.0025, w_SHV=0.9975.


Question:
Assets: XLY, PDBC
XLY: annualized_mean_return=0.4536, daily_std=0.0082
PDBC: annualized_mean_return=0.0756, daily_std=0.0080
Minimum required portfolio return (annualized): 0.3044
Market regime: sideways

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

Answer: w_XLY=0.6053, w_PDBC=0.3947

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000065 - 0.000001) / (0.000067 + 0.000065 - 0.000001)
  Unconstrained: w_XLY=0.4918
  After long-only clamp: w_XLY=0.4918, w_PDBC=0.5082.


Question:
Assets: XRP-USD, JNK
XRP-USD: annualized_mean_return=-2.5704, daily_std=0.0413
JNK: annualized_mean_return=0.0000, daily_std=0.0020
Minimum required portfolio return (annualized): -0.0015
Market regime: sideways

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

Answer: w_XRP-USD=0.0006, w_JNK=0.9994

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000004 - 0.000002) / (0.001704 + 0.000004 - 0.000005)
  Unconstrained: w_XRP-USD=0.0009
  After long-only clamp: w_XRP-USD=0.0009, w_JNK=0.9991.


Question:
Assets: XLK, BIL
XLK: annualized_mean_return=0.2772, daily_std=0.0087
BIL: annualized_mean_return=0.0000, daily_std=0.0002
Minimum required portfolio return (annualized): 0.1771
Market regime: sideways

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

Answer: w_XLK=0.6389, w_BIL=0.3611

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000076 + 0.000000 - 0.000000)
  Unconstrained: w_XLK=-0.0008
  After long-only clamp: w_XLK=0.0000, w_BIL=1.0000.


BTC-USD σ=0.0208, PALL σ=0.0148, ρ=0.024. Min-variance weights: BTC-USD=0.333, PALL=0.667.

Question:
Assets: BTC-USD, PALL
BTC-USD: annualized_mean_return=0.0504, daily_std=0.0208
PALL: annualized_mean_return=0.8064, daily_std=0.0148
Minimum required portfolio return (annualized): 0.7239
Market regime: sideways

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

Answer: w_BTC-USD=0.1091, w_PALL=0.8909

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000220 - 0.000007) / (0.000434 + 0.000220 - 0.000015)
  Unconstrained: w_BTC-USD=0.3328
  After long-only clamp: w_BTC-USD=0.3328, w_PALL=0.6672.


Question:
Assets: BTC-USD, EMB
BTC-USD: annualized_mean_return=-0.3780, daily_std=0.0281
EMB: annualized_mean_return=-0.0000, daily_std=0.0038
Minimum required portfolio return (annualized): -0.0411
Market regime: sideways

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

Answer: w_BTC-USD=0.0055, w_EMB=0.9945

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000014 - 0.000010) / (0.000791 + 0.000014 - 0.000020)
  Unconstrained: w_BTC-USD=0.0058
  After long-only clamp: w_BTC-USD=0.0058, w_EMB=0.9942.


Question:
Assets: XLK, CPER
XLK: annualized_mean_return=-0.0504, daily_std=0.0181
CPER: annualized_mean_return=0.4536, daily_std=0.0138
Minimum required portfolio return (annualized): 0.1481
Market regime: sideways

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

Answer: w_XLK=0.3205, w_CPER=0.6795

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000191 - 0.000069) / (0.000329 + 0.000191 - 0.000139)
  Unconstrained: w_XLK=0.3201
  After long-only clamp: w_XLK=0.3201, w_CPER=0.6799.


Question:
Assets: XLY, TLT
XLY: annualized_mean_return=0.1512, daily_std=0.0086
TLT: annualized_mean_return=0.1260, daily_std=0.0085
Minimum required portfolio return (annualized): 0.1350
Market regime: sideways

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

Answer: w_XLY=0.4925, w_TLT=0.5075

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000071 - -0.000009) / (0.000074 + 0.000071 - -0.000019)
  Unconstrained: w_XLY=0.4926
  After long-only clamp: w_XLY=0.4926, w_TLT=0.5074.


Question:
Assets: QUAL, REZ
QUAL: annualized_mean_return=0.2268, daily_std=0.0049
REZ: annualized_mean_return=-0.0000, daily_std=0.0114
Minimum required portfolio return (annualized): 0.2229
Market regime: sideways

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

Answer: w_QUAL=0.9828, w_REZ=0.0172

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000131 - 0.000014) / (0.000024 + 0.000131 - 0.000028)
  Unconstrained: w_QUAL=0.9177
  After long-only clamp: w_QUAL=0.9177, w_REZ=0.0823.


Question:
Assets: MTUM, TLH
MTUM: annualized_mean_return=0.0756, daily_std=0.0104
TLH: annualized_mean_return=0.2016, daily_std=0.0057
Minimum required portfolio return (annualized): 0.1945
Market regime: sideways

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

Answer: w_MTUM=0.0563, w_TLH=0.9437

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000033 - 0.000006) / (0.000108 + 0.000033 - 0.000012)
  Unconstrained: w_MTUM=0.2074
  After long-only clamp: w_MTUM=0.2074, w_TLH=0.7926.


MATIC-USD σ=0.0765, PALL σ=0.0211, ρ=-0.208. Min-variance weights: MATIC-USD=0.112, PALL=0.888.

Question:
Assets: MATIC-USD, PALL
MATIC-USD: annualized_mean_return=0.5544, daily_std=0.0765
PALL: annualized_mean_return=1.6632, daily_std=0.0211
Minimum required portfolio return (annualized): 1.4642
Market regime: sideways

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

Answer: w_MATIC-USD=0.1124, w_PALL=0.8876

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000447 - -0.000337) / (0.005855 + 0.000447 - -0.000674)
  Unconstrained: w_MATIC-USD=0.1124
  After long-only clamp: w_MATIC-USD=0.1124, w_PALL=0.8876.


Question:
Assets: BTC-USD, XLP
BTC-USD: annualized_mean_return=-0.7308, daily_std=0.0484
XLP: annualized_mean_return=-0.2520, daily_std=0.0101
Minimum required portfolio return (annualized): -0.2734
Market regime: sideways

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

Answer: w_BTC-USD=0.0000, w_XLP=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000102 - 0.000235) / (0.002346 + 0.000102 - 0.000470)
  Unconstrained: w_BTC-USD=-0.0673
  After long-only clamp: w_BTC-USD=0.0000, w_XLP=1.0000.


MATIC-USD σ=0.0640, STIP σ=0.0024, ρ=-0.115. Min-variance weights: MATIC-USD=0.006, STIP=0.994.

Question:
Assets: MATIC-USD, STIP
MATIC-USD: annualized_mean_return=3.0240, daily_std=0.0640
STIP: annualized_mean_return=0.0756, daily_std=0.0024
Minimum required portfolio return (annualized): 0.0912
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=0.0057, w_STIP=0.9943

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000006 - -0.000018) / (0.004099 + 0.000006 - -0.000035)
  Unconstrained: w_MATIC-USD=0.0056
  After long-only clamp: w_MATIC-USD=0.0056, w_STIP=0.9944.


Question:
Assets: XLU, BIL
XLU: annualized_mean_return=0.0504, daily_std=0.0116
BIL: annualized_mean_return=-0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): -0.0000
Market regime: sideways

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

Answer: w_XLU=0.0001, w_BIL=0.9999

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000135 + 0.000000 - -0.000001)
  Unconstrained: w_XLU=0.0030
  After long-only clamp: w_XLU=0.0030, w_BIL=0.9970.


Question:
Assets: XLB, REZ
XLB: annualized_mean_return=0.2268, daily_std=0.0152
REZ: annualized_mean_return=-0.1260, daily_std=0.0137
Minimum required portfolio return (annualized): -0.0518
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=0.3479, w_REZ=0.6521

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000188 - 0.000139) / (0.000231 + 0.000188 - 0.000279)
  Unconstrained: w_XLB=0.3469
  After long-only clamp: w_XLB=0.3469, w_REZ=0.6531.


Question:
Assets: VTI, ICSH
VTI: annualized_mean_return=-0.0756, daily_std=0.0068
ICSH: annualized_mean_return=-0.0000, daily_std=0.0007
Minimum required portfolio return (annualized): -0.0008
Market regime: sideways

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

Answer: w_VTI=0.0106, w_ICSH=0.9894

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000001) / (0.000046 + 0.000000 - -0.000001)
  Unconstrained: w_VTI=0.0237
  After long-only clamp: w_VTI=0.0237, w_ICSH=0.9763.


Question:
Assets: QQQ, HYG
QQQ: annualized_mean_return=0.4284, daily_std=0.0225
HYG: annualized_mean_return=0.1260, daily_std=0.0095
Minimum required portfolio return (annualized): 0.2979
Market regime: sideways

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

Answer: w_QQQ=0.5685, w_HYG=0.4315

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000091 - 0.000012) / (0.000507 + 0.000091 - 0.000024)
  Unconstrained: w_QQQ=0.1377
  After long-only clamp: w_QQQ=0.1377, w_HYG=0.8623.


MTUM σ=0.0195, ADA-USD σ=0.0677, ρ=0.357. Min-variance weights: MTUM=1.000, ADA-USD=0.000.

Question:
Assets: MTUM, ADA-USD
MTUM: annualized_mean_return=-0.2016, daily_std=0.0195
ADA-USD: annualized_mean_return=-1.9656, daily_std=0.0677
Minimum required portfolio return (annualized): -0.3726
Market regime: sideways

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

Answer: w_MTUM=1.0000, w_ADA-USD=0.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.004577 - 0.000472) / (0.000382 + 0.004577 - 0.000944)
  Unconstrained: w_MTUM=1.0224
  After long-only clamp: w_MTUM=1.0000, w_ADA-USD=0.0000.


Question:
Assets: BNB-USD, ITB
BNB-USD: annualized_mean_return=-0.3276, daily_std=0.0335
ITB: annualized_mean_return=0.3276, daily_std=0.0094
Minimum required portfolio return (annualized): 0.3205
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=0.0108, w_ITB=0.9892

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000087 - 0.000063) / (0.001122 + 0.000087 - 0.000127)
  Unconstrained: w_BNB-USD=0.0223
  After long-only clamp: w_BNB-USD=0.0223, w_ITB=0.9777.


Question:
Assets: VTI, BIL
VTI: annualized_mean_return=-0.1512, daily_std=0.0094
BIL: annualized_mean_return=0.0252, daily_std=0.0001
Minimum required portfolio return (annualized): -0.0550
Market regime: sideways

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

Answer: w_VTI=0.0001, w_BIL=0.9999

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000089 + 0.000000 - 0.000000)
  Unconstrained: w_VTI=-0.0008
  After long-only clamp: w_VTI=0.0000, w_BIL=1.0000.


Question:
Assets: XLI, ICSH
XLI: annualized_mean_return=-0.0504, daily_std=0.0086
ICSH: annualized_mean_return=0.0252, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0252
Market regime: sideways

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

Answer: w_XLI=-0.0000, w_ICSH=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000000) / (0.000074 + 0.000000 - -0.000000)
  Unconstrained: w_XLI=0.0036
  After long-only clamp: w_XLI=0.0036, w_ICSH=0.9964.


Question:
Assets: ETH-USD, CORN
ETH-USD: annualized_mean_return=-2.7216, daily_std=0.0472
CORN: annualized_mean_return=0.2268, daily_std=0.0084
Minimum required portfolio return (annualized): 0.1492
Market regime: sideways

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

Answer: w_ETH-USD=0.0263, w_CORN=0.9737

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000071 - -0.000015) / (0.002225 + 0.000071 - -0.000030)
  Unconstrained: w_ETH-USD=0.0369
  After long-only clamp: w_ETH-USD=0.0369, w_CORN=0.9631.


Question:
Assets: VEA, VNQ
VEA: annualized_mean_return=0.6552, daily_std=0.0104
VNQ: annualized_mean_return=0.1260, daily_std=0.0122
Minimum required portfolio return (annualized): 0.4624
Market regime: sideways

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

Answer: w_VEA=0.7337, w_VNQ=0.2663

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000148 - 0.000085) / (0.000108 + 0.000148 - 0.000170)
  Unconstrained: w_VEA=0.7328
  After long-only clamp: w_VEA=0.7328, w_VNQ=0.2672.


Question:
Assets: BTC-USD, VNQ
BTC-USD: annualized_mean_return=3.0240, daily_std=0.0507
VNQ: annualized_mean_return=0.1764, daily_std=0.0089
Minimum required portfolio return (annualized): 0.2254
Market regime: sideways

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

Answer: w_BTC-USD=0.0418, w_VNQ=0.9582

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000080 - -0.000034) / (0.002573 + 0.000080 - -0.000068)
  Unconstrained: w_BTC-USD=0.0419
  After long-only clamp: w_BTC-USD=0.0419, w_VNQ=0.9581.


Question:
Assets: VTI, ICSH
VTI: annualized_mean_return=0.1008, daily_std=0.0067
ICSH: annualized_mean_return=-0.0252, daily_std=0.0006
Minimum required portfolio return (annualized): -0.0245
Market regime: sideways

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

Answer: w_VTI=0.0088, w_ICSH=0.9912

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000045 + 0.000000 - 0.000001)
  Unconstrained: w_VTI=-0.0012
  After long-only clamp: w_VTI=0.0000, w_ICSH=1.0000.


Question:
Assets: ADA-USD, ICSH
ADA-USD: annualized_mean_return=0.8064, daily_std=0.1046
ICSH: annualized_mean_return=0.0000, daily_std=0.0004
Minimum required portfolio return (annualized): 0.0003
Market regime: sideways

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

Answer: w_ADA-USD=0.0004, w_ICSH=0.9996

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - -0.000004) / (0.010942 + 0.000000 - -0.000008)
  Unconstrained: w_ADA-USD=0.0004
  After long-only clamp: w_ADA-USD=0.0004, w_ICSH=0.9996.


Question:
Assets: ^VIX, DBB
^VIX: annualized_mean_return=-1.7136, daily_std=0.0920
DBB: annualized_mean_return=0.1260, daily_std=0.0080
Minimum required portfolio return (annualized): -0.9913
Market regime: sideways

Compute portfolio weights (w_^VIX, w_DBB) 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_DBB=X.XXXX

Answer: w_^VIX=0.0296, w_DBB=0.9704

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000063 - -0.000201) / (0.008463 + 0.000063 - -0.000403)
  Unconstrained: w_^VIX=0.0296
  After long-only clamp: w_^VIX=0.0296, w_DBB=0.9704.


Question:
Assets: BNB-USD, SLV
BNB-USD: annualized_mean_return=0.9072, daily_std=0.0555
SLV: annualized_mean_return=0.5040, daily_std=0.0086
Minimum required portfolio return (annualized): 0.5063
Market regime: sideways

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

Answer: w_BNB-USD=0.0061, w_SLV=0.9939

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000075 - 0.000056) / (0.003080 + 0.000075 - 0.000112)
  Unconstrained: w_BNB-USD=0.0061
  After long-only clamp: w_BNB-USD=0.0061, w_SLV=0.9939.


Question:
Assets: XLRE, SCHH
XLRE: annualized_mean_return=0.6048, daily_std=0.0092
SCHH: annualized_mean_return=0.5796, daily_std=0.0092
Minimum required portfolio return (annualized): 0.5979
Market regime: sideways

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

Answer: w_XLRE=0.7262, w_SCHH=0.2738

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000084 - 0.000083) / (0.000085 + 0.000084 - 0.000166)
  Unconstrained: w_XLRE=0.4674
  After long-only clamp: w_XLRE=0.4674, w_SCHH=0.5326.


Question:
Assets: IVV, ICSH
IVV: annualized_mean_return=0.2520, daily_std=0.0061
ICSH: annualized_mean_return=0.0252, daily_std=0.0002
Minimum required portfolio return (annualized): 0.0944
Market regime: sideways

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

Answer: w_IVV=0.3051, w_ICSH=0.6949

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000038 + 0.000000 - 0.000000)
  Unconstrained: w_IVV=-0.0047
  After long-only clamp: w_IVV=0.0000, w_ICSH=1.0000.


Question:
Assets: XLE, XHB
XLE: annualized_mean_return=1.0332, daily_std=0.0214
XHB: annualized_mean_return=-0.4788, daily_std=0.0222
Minimum required portfolio return (annualized): 0.1518
Market regime: sideways

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

Answer: w_XLE=0.5184, w_XHB=0.4816

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000491 - 0.000021) / (0.000458 + 0.000491 - 0.000042)
  Unconstrained: w_XLE=0.5183
  After long-only clamp: w_XLE=0.5183, w_XHB=0.4817.


Question:
Assets: ETH-USD, EMB
ETH-USD: annualized_mean_return=3.8304, daily_std=0.0711
EMB: annualized_mean_return=0.0756, daily_std=0.0019
Minimum required portfolio return (annualized): 0.0756
Market regime: sideways

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

Answer: w_ETH-USD=0.0000, w_EMB=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000004 - 0.000025) / (0.005051 + 0.000004 - 0.000051)
  Unconstrained: w_ETH-USD=-0.0043
  After long-only clamp: w_ETH-USD=0.0000, w_EMB=1.0000.


Question:
Assets: EEM, PDBC
EEM: annualized_mean_return=0.3528, daily_std=0.0081
PDBC: annualized_mean_return=-0.2520, daily_std=0.0076
Minimum required portfolio return (annualized): -0.0325
Market regime: sideways

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

Answer: w_EEM=0.4620, w_PDBC=0.5380

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000057 - 0.000002) / (0.000066 + 0.000057 - 0.000004)
  Unconstrained: w_EEM=0.4621
  After long-only clamp: w_EEM=0.4621, w_PDBC=0.5379.


Question:
Assets: IVV, SCHP
IVV: annualized_mean_return=0.1512, daily_std=0.0063
SCHP: annualized_mean_return=0.0504, daily_std=0.0018
Minimum required portfolio return (annualized): 0.0578
Market regime: sideways

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

Answer: w_IVV=0.1447, w_SCHP=0.8553

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000003 - -0.000004) / (0.000040 + 0.000003 - -0.000007)
  Unconstrained: w_IVV=0.1380
  After long-only clamp: w_IVV=0.1380, w_SCHP=0.8620.


Question:
Assets: XRP-USD, IAU
XRP-USD: annualized_mean_return=-0.9576, daily_std=0.0492
IAU: annualized_mean_return=0.2772, daily_std=0.0101
Minimum required portfolio return (annualized): -0.4204
Market regime: sideways

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

Answer: w_XRP-USD=0.0118, w_IAU=0.9882

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000103 - 0.000075) / (0.002419 + 0.000103 - 0.000150)
  Unconstrained: w_XRP-USD=0.0118
  After long-only clamp: w_XRP-USD=0.0118, w_IAU=0.9882.


Question:
Assets: ADA-USD, ITB
ADA-USD: annualized_mean_return=3.2256, daily_std=0.0766
ITB: annualized_mean_return=0.6552, daily_std=0.0194
Minimum required portfolio return (annualized): 0.6952
Market regime: sideways

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

Answer: w_ADA-USD=0.0199, w_ITB=0.9801

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000375 - 0.000261) / (0.005862 + 0.000375 - 0.000522)
  Unconstrained: w_ADA-USD=0.0199
  After long-only clamp: w_ADA-USD=0.0199, w_ITB=0.9801.


Question:
Assets: FXI, LQD
FXI: annualized_mean_return=-0.3528, daily_std=0.0156
LQD: annualized_mean_return=0.1260, daily_std=0.0032
Minimum required portfolio return (annualized): 0.0424
Market regime: sideways

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

Answer: w_FXI=0.0744, w_LQD=0.9256

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000010 - -0.000010) / (0.000244 + 0.000010 - -0.000019)
  Unconstrained: w_FXI=0.0735
  After long-only clamp: w_FXI=0.0735, w_LQD=0.9265.


MATIC-USD σ=0.0738, SCHP σ=0.0053, ρ=0.151. Min-variance weights: MATIC-USD=0.000, SCHP=1.000.

Question:
Assets: MATIC-USD, SCHP
MATIC-USD: annualized_mean_return=0.5040, daily_std=0.0738
SCHP: annualized_mean_return=-0.1260, daily_std=0.0053
Minimum required portfolio return (annualized): -0.1260
Market regime: sideways

Compute portfolio weights (w_MATIC-USD, w_SCHP) 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_SCHP=X.XXXX

Answer: w_MATIC-USD=0.0000, w_SCHP=1.0000

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000029 - 0.000059) / (0.005442 + 0.000029 - 0.000119)
  Unconstrained: w_MATIC-USD=-0.0058
  After long-only clamp: w_MATIC-USD=0.0000, w_SCHP=1.0000.


EEM σ=0.0107, LINK-USD σ=0.0560, ρ=0.050. Min-variance weights: EEM=0.974, LINK-USD=0.026.

Question:
Assets: EEM, LINK-USD
EEM: annualized_mean_return=-0.3024, daily_std=0.0107
LINK-USD: annualized_mean_return=4.6368, daily_std=0.0560
Minimum required portfolio return (annualized): -0.2104
Market regime: sideways

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

Answer: w_EEM=0.9735, w_LINK-USD=0.0265

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.003133 - 0.000030) / (0.000115 + 0.003133 - 0.000060)
  Unconstrained: w_EEM=0.9735
  After long-only clamp: w_EEM=0.9735, w_LINK-USD=0.0265.


Question:
Assets: EFA, STIP
EFA: annualized_mean_return=-0.1008, daily_std=0.0063
STIP: annualized_mean_return=0.0252, daily_std=0.0007
Minimum required portfolio return (annualized): -0.0500
Market regime: sideways

Compute portfolio weights (w_EFA, w_STIP) 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_STIP=X.XXXX

Answer: w_EFA=0.0118, w_STIP=0.9882

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.000040 + 0.000000 - 0.000001)
  Unconstrained: w_EFA=0.0051
  After long-only clamp: w_EFA=0.0051, w_STIP=0.9949.


Question:
Assets: QQQ, EMB
QQQ: annualized_mean_return=0.1512, daily_std=0.0083
EMB: annualized_mean_return=0.0000, daily_std=0.0036
Minimum required portfolio return (annualized): 0.0922
Market regime: sideways

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

Answer: w_QQQ=0.6098, w_EMB=0.3902

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000013 - 0.000001) / (0.000068 + 0.000013 - 0.000002)
  Unconstrained: w_QQQ=0.1560
  After long-only clamp: w_QQQ=0.1560, w_EMB=0.8440.


Question:
Assets: VEA, CPER
VEA: annualized_mean_return=-0.1260, daily_std=0.0065
CPER: annualized_mean_return=-0.0252, daily_std=0.0140
Minimum required portfolio return (annualized): -0.0672
Market regime: sideways

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

Answer: w_VEA=0.4167, w_CPER=0.5833

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000196 - 0.000023) / (0.000042 + 0.000196 - 0.000046)
  Unconstrained: w_VEA=0.9016
  After long-only clamp: w_VEA=0.9016, w_CPER=0.0984.


Question:
Assets: VTI, SOYB
VTI: annualized_mean_return=-0.3276, daily_std=0.0102
SOYB: annualized_mean_return=-0.1260, daily_std=0.0081
Minimum required portfolio return (annualized): -0.1524
Market regime: sideways

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

Answer: w_VTI=0.1310, w_SOYB=0.8690

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000066 - -0.000004) / (0.000105 + 0.000066 - -0.000007)
  Unconstrained: w_VTI=0.3919
  After long-only clamp: w_VTI=0.3919, w_SOYB=0.6081.


Question:
Assets: DOT-USD, DBB
DOT-USD: annualized_mean_return=2.7720, daily_std=0.0724
DBB: annualized_mean_return=0.4536, daily_std=0.0104
Minimum required portfolio return (annualized): 1.4877
Market regime: sideways

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

Answer: w_DOT-USD=0.4460, w_DBB=0.5540

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000109 - -0.000030) / (0.005246 + 0.000109 - -0.000060)
  Unconstrained: w_DOT-USD=0.0256
  After long-only clamp: w_DOT-USD=0.0256, w_DBB=0.9744.


Question:
Assets: ETH-USD, EMB
ETH-USD: annualized_mean_return=3.9816, daily_std=0.0529
EMB: annualized_mean_return=0.1260, daily_std=0.0039
Minimum required portfolio return (annualized): 2.0957
Market regime: sideways

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

Answer: w_ETH-USD=0.5109, w_EMB=0.4891

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000015 - 0.000012) / (0.002802 + 0.000015 - 0.000024)
  Unconstrained: w_ETH-USD=0.0012
  After long-only clamp: w_ETH-USD=0.0012, w_EMB=0.9988.


Question:
Assets: ADA-USD, IYR
ADA-USD: annualized_mean_return=8.7192, daily_std=0.0846
IYR: annualized_mean_return=0.2520, daily_std=0.0096
Minimum required portfolio return (annualized): 4.8296
Market regime: sideways

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

Answer: w_ADA-USD=0.5406, w_IYR=0.4594

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000093 - -0.000137) / (0.007166 + 0.000093 - -0.000274)
  Unconstrained: w_ADA-USD=0.0305
  After long-only clamp: w_ADA-USD=0.0305, w_IYR=0.9695.


Question:
Assets: VTI, TLH
VTI: annualized_mean_return=0.4284, daily_std=0.0053
TLH: annualized_mean_return=-0.1260, daily_std=0.0042
Minimum required portfolio return (annualized): 0.3604
Market regime: sideways

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

Answer: w_VTI=0.8773, w_TLH=0.1227

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000018 - -0.000005) / (0.000028 + 0.000018 - -0.000009)
  Unconstrained: w_VTI=0.4093
  After long-only clamp: w_VTI=0.4093, w_TLH=0.5907.


Question:
Assets: XRP-USD, IVV
XRP-USD: annualized_mean_return=0.0000, daily_std=0.0369
IVV: annualized_mean_return=0.0756, daily_std=0.0120
Minimum required portfolio return (annualized): 0.0725
Market regime: sideways

Compute portfolio weights (w_XRP-USD, w_IVV) 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_IVV=X.XXXX

Answer: w_XRP-USD=0.0410, w_IVV=0.9590

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000144 - 0.000044) / (0.001363 + 0.000144 - 0.000088)
  Unconstrained: w_XRP-USD=0.0705
  After long-only clamp: w_XRP-USD=0.0705, w_IVV=0.9295.


Question:
Assets: ACWI, DOT-USD
ACWI: annualized_mean_return=0.2268, daily_std=0.0097
DOT-USD: annualized_mean_return=-0.9828, daily_std=0.0581
Minimum required portfolio return (annualized): 0.2077
Market regime: sideways

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

Answer: w_ACWI=0.9842, w_DOT-USD=0.0158

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.003371 - -0.000063) / (0.000095 + 0.003371 - -0.000127)
  Unconstrained: w_ACWI=0.9560
  After long-only clamp: w_ACWI=0.9560, w_DOT-USD=0.0440.


Question:
Assets: FXI, SOL-USD
FXI: annualized_mean_return=0.3528, daily_std=0.0164
SOL-USD: annualized_mean_return=1.0584, daily_std=0.0531
Minimum required portfolio return (annualized): 0.6542
Market regime: sideways

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

Answer: w_FXI=0.5728, w_SOL-USD=0.4272

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.002823 - 0.000067) / (0.000267 + 0.002823 - 0.000134)
  Unconstrained: w_FXI=0.9322
  After long-only clamp: w_FXI=0.9322, w_SOL-USD=0.0678.


Question:
Assets: EEM, SCHP
EEM: annualized_mean_return=-0.1008, daily_std=0.0110
SCHP: annualized_mean_return=-0.1260, daily_std=0.0034
Minimum required portfolio return (annualized): -0.1106
Market regime: sideways

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

Answer: w_EEM=0.6111, w_SCHP=0.3889

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000012 - 0.000005) / (0.000120 + 0.000012 - 0.000011)
  Unconstrained: w_EEM=0.0532
  After long-only clamp: w_EEM=0.0532, w_SCHP=0.9468.


Question:
Assets: ETH-USD, BIL
ETH-USD: annualized_mean_return=0.7560, daily_std=0.0345
BIL: annualized_mean_return=-0.0000, daily_std=0.0001
Minimum required portfolio return (annualized): 0.5273
Market regime: sideways

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

Answer: w_ETH-USD=0.6975, w_BIL=0.3025

Explanation:
Analytic min-variance formula:
  w1* = (σ2² - σ12) / (σ1² + σ2² - 2σ12)
  = (0.000000 - 0.000000) / (0.001193 + 0.000000 - 0.000000)
  Unconstrained: w_ETH-USD=-0.0001
  After long-only clamp: w_ETH-USD=0.0000, w_BIL=1.0000.